Journal articles on the topic 'Test error estimation'

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1

Wang, Haiying, Xinping Wang, Chao Wang, and Jian Xu. "Concrete Compression Test Data Estimation Based on a Wavelet Neural Network Model." Mathematical Problems in Engineering 2019 (February 11, 2019): 1–10. http://dx.doi.org/10.1155/2019/4952036.

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Firstly, a genetic algorithm (GA) and simulated annealing (SA) optimized fuzzy c-means clustering algorithm (FCM) was proposed in this paper, which was developed to allow for a clustering analysis of the massive concrete cube specimen compression test data. Then, using an optimized error correction time series estimation method based on the wavelet neural network (WNN), a concrete cube specimen compressive strength test data estimation model was constructed. Taking the results of cluster analysis as data samples, the short-term accurate estimation of concrete quality was carried out. It was found that the mean absolute percentage error, e1, and the root mean square error, e2, for the samples were 6.03385% and 3.3682KN, indicating that the proposed method had higher estimation accuracy and was suitable for concrete compressive test data short-term quality estimations.
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ODEN, J. TINSLEY, SERGE PRUDHOMME, TIM WESTERMANN, JON BASS, and MARK E. BOTKIN. "ERROR ESTIMATION OF EIGENFREQUENCIES FOR ELASTICITY AND SHELL PROBLEMS." Mathematical Models and Methods in Applied Sciences 13, no. 03 (March 2003): 323–44. http://dx.doi.org/10.1142/s0218202503002520.

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In this paper, a method for deriving computable estimates of the approximation error in eigenvalues or eigenfrequencies of three-dimensional linear elasticity or shell problems is presented. The analysis for the error estimator follows the general approach of goal-oriented error estimation for which the error is estimated in so-called quantities of interest, here the eigenfrequencies, rather than global norms. A general theory is developed and is then applied to the linear elasticity equations. For the shell analysis, it is assumed that the shell model is not completely known and additional errors are introduced due to modeling approximations. The approach is then based on recovering three-dimensional approximations from the shell eigensolution and employing the error estimator developed for linear elasticity. The performance of the error estimator is demonstrated on several test problems.
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3

Weiss, Andrew A. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation." Econometric Theory 7, no. 1 (March 1991): 46–68. http://dx.doi.org/10.1017/s0266466600004230.

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We consider least absolute error estimation in a dynamic nonlinear model with neither independent nor identically distributed errors. The estimator is shown to be consistent and asymptotically normal, with asymptotic covariance matrix depending on the errors through the heights of their density functions at their medians (zero). A consistent estimator of the asymptotic covariance matrix of the estimator is given, and the Wald, Lagrange multiplier, and likelihood ratio tests for linear restrictions on the parameters are discussed. A Lagrange multiplier test for heteroscedasticity based upon the absolute residuals is analyzed. This will be useful whenever the heights of the density functions are related to the dispersions.
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Wee, Seungwoo, Changryoul Choi, and Jechang Jeong. "Blind Interleaver Parameters Estimation Using Kolmogorov–Smirnov Test." Sensors 21, no. 10 (May 15, 2021): 3458. http://dx.doi.org/10.3390/s21103458.

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The use of error-correcting codes (ECCs) is essential for designing reliable digital communication systems. Usually, most systems correct errors under cooperative environments. If receivers do not know interleaver parameters, they must first find out them to decode. In this paper, a blind interleaver parameters estimation method is proposed using the Kolmogorov–Smirnov (K–S) test. We exploit the fact that rank distributions of square matrices of linear codes differ from those of random sequences owing to the linear dependence of linear codes. We use the K–S test to make decision whether two groups are extracted from the same distribution. The K–S test value is used as a measure to find the most different rank distribution for the blind interleaver parameters estimation. In addition to control false alarm rates, multinomial distribution is used to calculate the probability that the most different rank distribution will occur. By exploiting those, we can estimate the interleaver period with relatively low complexity. Experimental results show that the proposed algorithm outperforms previous methods regardless of the bit error rate.
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Spenceley, S. E., and D. B. Henson. "Visual field test simulation and error in threshold estimation." British Journal of Ophthalmology 80, no. 4 (April 1, 1996): 304–8. http://dx.doi.org/10.1136/bjo.80.4.304.

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6

Giles, David E. A. "Pre-test estimation in regression under absolute error loss." Economics Letters 41, no. 4 (January 1993): 339–43. http://dx.doi.org/10.1016/0165-1765(93)90202-n.

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7

Saputri, Ovi Delviyanti, Ferra Yanuar, and Dodi Devianto. "Simulation Study The Implementation of Quantile Bootstrap Method on Autocorrelated Error." CAUCHY 5, no. 3 (December 5, 2018): 95. http://dx.doi.org/10.18860/ca.v5i3.5349.

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<span lang="DE">Quantile regression is a regression method with the approach of separating or dividing data into certain quantiles by minimizing the number of absolute values from asymmetrical errors to overcome unfulfilled assumptions, including the presence of autocorrelation. The resulting model parameters are tested for accuracy using the bootstrap method. The bootstrap method is a parameter estimation method by re-sampling from the original sample as much as R replication. The bootstrap trust interval was then used as a test consistency test algorithm constructed on the estimator by the quantile regression method. And test the uncommon quantile regression method with bootstrap method. The data obtained in this test is data replication 10 times. The biasness is calculated from the difference between the quantile estimate and bootstrap estimation. Quantile estimation methods are said to be unbiased if the standard deviation bias is less than the standard bootstrap deviation. This study proves that the estimated value with quantile regression is within the bootstrap percentile confidence interval and proves that 10 times replication produces a better estimation value compared to other replication measures. Quantile regression method in this study is also able to produce unbiased parameter estimation values.</span>
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8

Huang, Liang, Cheng Chen, Tong Guo, and Menghui Chen. "Discrete Tangent Stiffness Estimation Method for Pseudo Dynamic Test." International Journal of Structural Stability and Dynamics 19, no. 01 (December 20, 2018): 1940014. http://dx.doi.org/10.1142/s0219455419400145.

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In pseudo dynamic (PSD) test, researchers have long recognized the importance and potential benefits of utilizing the tangent stiffness of experimental specimen to correct the restoring force and analyze the energy error. However, improving accuracy and efficiency of the instantaneous stiffness estimation still presents a challenge. Based on the theory of discrete curve parameter recognition and the geometrical analysis approach, this paper proposes a discrete tangent stiffness estimation (DTSE) method to estimate the instantaneous tangent stiffness of a single degree of freedom (SDOF) experimental specimen. For different magnitudes of measurement noise, the proposed method can adaptively select and retain a series of latest valid data and ignore outdated information, of which the advantage is highly improving the accuracy and promptness of instantaneous stiffness estimation. The numerical study shows that the DTSE method has better accuracy and promptness of tangent stiffness estimation when compared with other existing methods. In a PSD test involving a sliding isolator, the DTSE method is utilized to analyze the cumulative energy error, the result of which shows the cumulative energy error is negative and decreases gradually. The analysis of experimental results demonstrates that the undershooting error of actuator added extra energy into the PSD testing system. Thus, the proposed method provides a desirable solution to instantaneous stiffness estimation.
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Qi, Gengxin, Xiaobin Fan, and Hao Li. "A comparative study of the unscented Kalman filter and particle filter estimation methods for the measurement of the road adhesion coefficient." Mechanical Sciences 13, no. 2 (August 25, 2022): 735–49. http://dx.doi.org/10.5194/ms-13-735-2022.

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Abstract. The measurement of the road adhesion coefficient is of great significance for the vehicle active safety control system and is one of the key technologies for future autonomous driving. With a focus on the problems of interference uncertainty and system nonlinearity in the estimation of the road adhesion coefficient, this work adopts a vehicle model with 7 degrees of freedom (7-DOF) and the Dugoff tire model and uses these models to estimate the road adhesion coefficient in real time based on the particle filter (PF) algorithm. The estimations using the PF algorithm are verified by selecting typical working conditions, and they are compared with estimations using the unscented Kalman filter (UKF) algorithm. Simulation results show that the road adhesion coefficient estimator error based on the UKF algorithm is less than 7 %, whereas the road adhesion coefficient estimator error based on the PF algorithm is less than 0.1 %. Thus, compared with the UKF algorithm, the PF algorithm has a higher accuracy and control effect with respect to estimating the road adhesion coefficient under different road conditions. In order to verify the robustness of the road adhesion coefficient estimator, an automobile test platform based on a four-wheel-hub-motor car is built. According to the experimental results, the estimator based on the PF algorithm can realize the road surface identification with an error of less than 1 %, which verifies the feasibility and effectiveness of the algorithm with respect to estimating the road adhesion coefficient and shows good robustness.
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Ma, Chao, Chun Jie Qiao, Yue Ke Wang, and Shen Zhao. "A New Method for Target Motion Analysis." Applied Mechanics and Materials 336-338 (July 2013): 2354–58. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.2354.

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The paper proposes a new method for a targets trajectory, assumed to be linear and uniform, based on the observation of its speed and bearings. After introducing the new method based on assumed model, the paper analyzes the relative error of range estimation caused by speed and bearings estimations relative error; The results of target motion analysis (TMA) is optimized by linearizing the model and using kalman filter. Pond test shows that relative error of range estimation calculated by this method is less than 10-1.
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Weiss, Andrew A. "A Comparison of Ordinary Least Squares and Least Absolute Error Estimation." Econometric Theory 4, no. 3 (December 1988): 517–27. http://dx.doi.org/10.1017/s0266466600013438.

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In a linear-regression model with heteroscedastic errors, we consider two tests: a Hausman test comparing the ordinary least squares (OLS) and least absolute error (LAE) estimators and a test based on the signs of the errors from OLS. It turns out that these are related by the well-known equivalence between Hausman and the generalized method of moments tests. Particular cases, including homoscedasticity and asymmetry in the errors, are discussed.
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Clarke, Judith A., David E. A. Giles, and T. Dudley Wallace. "Preliminary-Test Estimation of the Error Variance in Linear Regression." Econometric Theory 3, no. 2 (April 1987): 299–304. http://dx.doi.org/10.1017/s0266466600010355.

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We derive exact finite-sample expressions for the biases and risks of several common pretest estimators of the scale parameter in the linear regression model. These estimators are associated with least squares, maximum likelihood and minimum mean squared error component estimators. Of these three criteria, the last is found to be superior (in terms of risk under quadratic loss) when pretesting in typical situations.
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13

Hintz-Madsen, Mads, Lars Kai Hansen, Jan Larsen, Morten With Pedersen, and Michael Larsen. "Neural classifier construction using regularization, pruning and test error estimation." Neural Networks 11, no. 9 (December 1998): 1659–70. http://dx.doi.org/10.1016/s0893-6080(98)00093-8.

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14

Jiang, Yinfeng, Wenxiang Song, Hao Zhu, Yun Zhu, Yongzhi Du, and Huichun Yin. "Extended Rauch–Tung–Striebel Smoother for the State of Charge Estimation of Lithium-Ion Batteries Based on an Enhanced Circuit Model." Energies 15, no. 3 (January 28, 2022): 963. http://dx.doi.org/10.3390/en15030963.

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The state of charge (SOC) of a lithium battery system is critical since it indicates the remaining operating hours, full charge time, and peak power of the battery. This paper recommends an extended Rauch–Tung–Striebel smoother (ERTSS) for estimating SOC. It is implemented based on an improved equivalent circuit model with hysteresis voltage. The smoothing step of ERTSS will reduce the estimation error further. Additionally, the genetic algorithm (GA) is employed for searching the optimal ERTSS’s smoothing time interval. Various dynamic cell tests are conducted to verify the model’s accuracy and error estimation deviation. The test results demonstrate that ERTSS’s SOC estimation error is limited to 4% with an initial error between −25 ∘C and 45 ∘C and that the root mean square error (RMSE) of ERTSS’s SOC estimation is approximately 5% lower than that of extended Kalman filter (EKF). The ERTSS improves the SOC estimation accuracy at all operating temperatures of batteries.
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Miao, Maoke, Weiwei Cai, and Xiaofeng Li. "Parameter Estimation of Gamma-Gamma Fading with Generalized Pointing Errors in FSO Systems." Wireless Communications and Mobile Computing 2021 (July 16, 2021): 1–14. http://dx.doi.org/10.1155/2021/1301878.

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In this paper, the challenges of parameter estimation for the Gamma-Gamma turbulence channels with generalized pointing errors are addressed. The Kolmogorov-Smirnov goodness-of-fit statistical test results indicate that the approximate probability density function obtained by the saddlepoint approximation (SAP) method provides a better approximation for a larger value w z , and this means that the proposed method is more efficient for the FSO links over long distances when the transmit divergence angle at the transmitter side is fixed. Also, an additional parameter k needs to be estimated in addition to the shaping parameters α and β under the SAP method. An estimation scheme for the shaping parameters is proposed based on the SAP method. The performance of the proposed estimation is investigated by using the mean square error (MSE) and normalized mean square error (NMSE). The results indicate the proposed estimator exhibits satisfactory performance in both noiseless and noisy environments. The effects of the receiver aperture on the estimation performance are also discussed.
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16

Silvapulle, Mervyn J. "On Limited Dependent Variable Models: Maximum Likelihood Estimation and Test of One-sided Hypothesis." Econometric Theory 7, no. 3 (September 1991): 385–95. http://dx.doi.org/10.1017/s0266466600004527.

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The limited dependent variable models with errors having log-concave density functions are studied here. For such models with normal errors, the asymptotic normality of the maximum likelihood estimator was established by Amemiya [1]. We show, when the density of the error distribution is log-concave, that the maximum likelihood estimator exists with arbitrarily large probability for large sample sizes, and is asymptotically normal. The general theory presented here includes the important special cases of normal, logistic, and extreme value error distributions. The main results are established under rather weak conditions. It is also shown that, under the null hypothesis, the asymptotic distribution of the likelihood ratio statistic for testing a one-sided alternative hypothesis is a weighted sum of chi-squares.
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Sakai, Katsuya, Tsubasa Kawasaki, Yumi Ikeda, Keita Tominaga, and Kohei Kurihara. "Relationship between Motor Estimation Error and Physical Function in Patients with Parkinson’s Disease." Medicines 7, no. 8 (July 28, 2020): 43. http://dx.doi.org/10.3390/medicines7080043.

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Background: Motor estimation error is an index of how accurately one’s body movement is recognized. This study determines whether motor estimation error distance is a Parkinson’s disease (PD)- or age-related disability using a two-step task. Methods: The participants were 19 PD patients and 58 elderly people with disabilities. A two-step prediction test and an actual two-step test were performed. The motor estimation error distance (prediction of two-step distance minus actual two-step distance) and error rate between the two groups were compared. We conducted a correlation analysis between the motor estimation error and clinical factor (e.g., Hoehn and Yahr stage (H & Y), Unified Parkinson’s Disease Rating Scale (UPDRS)) related to PD. Results: The motor estimation error distance was not significantly different between the PD patient group and the elderly group with disabilities. However, significant correlations between motor estimation error and H & Y, and between motor estimation error and UPDRS part II, were observed. The error rate was significantly correlated with the Fall Efficacy Scale. Conclusions: The motor estimation error distance is influenced by both aging and PD.
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Biscarri, F., A. Menéndez, and A. Molina. "Flowmeter random error estimation by an analytical variance estimation method: a simple test bed." Control Engineering Practice 12, no. 7 (July 2004): 857–63. http://dx.doi.org/10.1016/j.conengprac.2003.10.005.

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Altman, Eitan, Izza Mounir, Fatim-Zahra Najid, and Samir M. Perlaza. "On the True Number of COVID-19 Infections: Effect of Sensitivity, Specificity and Number of Tests on Prevalence Ratio Estimation." International Journal of Environmental Research and Public Health 17, no. 15 (July 24, 2020): 5328. http://dx.doi.org/10.3390/ijerph17155328.

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In this paper, a formula for estimating the prevalence ratio of a disease in a population that is tested with imperfect tests is given. The formula is in terms of the fraction of positive test results and test parameters, i.e., probability of true positives (sensitivity) and the probability of true negatives (specificity). The motivation of this work arises in the context of the COVID-19 pandemic in which estimating the number of infected individuals depends on the sensitivity and specificity of the tests. In this context, it is shown that approximating the prevalence ratio by the ratio between the number of positive tests and the total number of tested individuals leads to dramatically high estimation errors, and thus, unadapted public health policies. The relevance of estimating the prevalence ratio using the formula presented in this work is that precision increases with the number of tests. Two conclusions are drawn from this work. First, in order to ensure that a reliable estimation is achieved with a finite number of tests, testing campaigns must be implemented with tests for which the sum of the sensitivity and the specificity is sufficiently different than one. Second, the key parameter for reducing the estimation error is the number of tests. For a large number of tests, as long as the sum of the sensitivity and specificity is different than one, the exact values of these parameters have very little impact on the estimation error.
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Hogan, Thomas P., Laurie A. Wyckoff, Paul Krebs, William Jones, and Mark P. Fitzgerald. "Tolerance for Error and Computational Estimation Ability." Psychological Reports 94, no. 3_suppl (June 2004): 1393–403. http://dx.doi.org/10.2466/pr0.94.3c.1393-1403.

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Previous investigators have suggested that the personality variable tolerance for error is related to success in computational estimation. However, this suggestion has not been tested directly. This study examined the relationship between performance on a computational estimation test and scores on the NEO–Five Factor Inventory, a measure of the Big Five personality traits, including Openness, an index of tolerance for ambiguity. Other variables included SAT–I Verbal and Mathematics scores and self-rated mathematics ability. Participants were 65 college students. There was no significant relationship between the tolerance variable and computational estimation performance. There was a modest negative relationship between Agreeableness and estimation performance. The skepticism associated with the negative pole of the Agreeableness dimension may be important to pursue in further understanding of estimation ability.
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Reina, Salvatore, Robert Arcos, Arnau Clot, and Jordi Romeu. "An Efficient Experimental Methodology for the Assessment of the Dynamic Behaviour of Resilient Elements." Materials 13, no. 13 (June 27, 2020): 2889. http://dx.doi.org/10.3390/ma13132889.

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The assessment of the dynamic behaviour of resilient elements can be performed using the indirect method as described in the standard ISO 10846-3. This paper presents a methodology for control the error on the estimation of the frequency response functions (FRF) required for the application of the indirect method when sweep sine excitation is used. Based on a simulation process, this methodology allows for the design of the sweep sine excitation parameters, i.e., the sweep rate and the force amplitude, to control three types of errors associated to the experimentally obtained FRF in the presence of background noise: a general error of the FRF in a selected frequency range, and the errors associated to the amplitude and the frequency of the FRF resonance peak. The signal processing method used can be also tested with this methodology. The methodology has been tested in the characterisation of two different resilient elements: an elastomer and a coil spring. The simulated error estimations has been found to be in good agreement with the errors found in the measured FRF. Furthermore, it is found that for large signal-to-noise ratios, both sweep rate and force amplitude significantly affect the FRF estimation error, while, for small signal-to-noise ratios, only the force amplitude can control the error efficiently. The current methodology is specially interesting for laboratory test rigs highly used for the dynamic characterisation of resilient elements which are required to operate efficiently, since it can be used for minimising test times and providing quality assurance. Moreover, the application of this methodology would be specially relevant when characterisation is done in noisy environments.
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Chen, Haiqiang. "ROBUST ESTIMATION AND INFERENCE FOR THRESHOLD MODELS WITH INTEGRATED REGRESSORS." Econometric Theory 31, no. 4 (October 27, 2014): 778–810. http://dx.doi.org/10.1017/s0266466614000553.

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This paper studies the robust estimation and inference of threshold models with integrated regressors. We derive the asymptotic distribution of the profiled least squares (LS) estimator under the diminishing threshold effect assumption that the size of the threshold effect converges to zero. Depending on how rapidly this sequence converges, the model may be identified or only weakly identified and asymptotic theorems are developed for both cases. As the convergence rate is unknown in practice, a model-selection procedure is applied to determine the model identification strength and to construct robust confidence intervals, which have the correct asymptotic size irrespective of the magnitude of the threshold effect. The model is then generalized to incorporate endogeneity and serial correlation in error terms, under which, we design a Cochrane–Orcutt feasible generalized least squares (FGLS) estimator which enjoys efficiency gains and robustness against different error specifications, including both I(0) and I(1) errors. Based on this FGLS estimator, we further develop a sup-Wald statistic to test for the existence of the threshold effect. Monte Carlo simulations show that our estimators and test statistics perform well.
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Jiang, Haobin, Xijia Chen, Yifu Liu, Qian Zhao, Huanhuan Li, and Biao Chen. "Online State-of-Charge Estimation Based on the Gas–Liquid Dynamics Model for Li(NiMnCo)O2 Battery." Energies 14, no. 2 (January 8, 2021): 324. http://dx.doi.org/10.3390/en14020324.

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Accurately estimating the online state-of-charge (SOC) of the battery is one of the crucial issues of the battery management system. In this paper, the gas–liquid dynamics (GLD) battery model with direct temperature input is selected to model Li(NiMnCo)O2 battery. The extended Kalman Filter (EKF) algorithm is elaborated to couple the offline model and online model to achieve the goal of quickly eliminating initial errors in the online SOC estimation. An implementation of the hybrid pulse power characterization test is performed to identify the offline parameters and determine the open-circuit voltage vs. SOC curve. Apart from the standard cycles including Constant Current cycle, Federal Urban Driving Schedule cycle, Urban Dynamometer Driving Schedule cycle and Dynamic Stress Test cycle, a combined cycle is constructed for experimental validation. Furthermore, the study of the effect of sampling time on estimation accuracy and the robustness analysis of the initial value are carried out. The results demonstrate that the proposed method realizes the accurate estimation of SOC with a maximum mean absolute error at 0.50% in five working conditions and shows strong robustness against the sparse sampling and input error.
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Jiang, Haobin, Xijia Chen, Yifu Liu, Qian Zhao, Huanhuan Li, and Biao Chen. "Online State-of-Charge Estimation Based on the Gas–Liquid Dynamics Model for Li(NiMnCo)O2 Battery." Energies 14, no. 2 (January 8, 2021): 324. http://dx.doi.org/10.3390/en14020324.

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Accurately estimating the online state-of-charge (SOC) of the battery is one of the crucial issues of the battery management system. In this paper, the gas–liquid dynamics (GLD) battery model with direct temperature input is selected to model Li(NiMnCo)O2 battery. The extended Kalman Filter (EKF) algorithm is elaborated to couple the offline model and online model to achieve the goal of quickly eliminating initial errors in the online SOC estimation. An implementation of the hybrid pulse power characterization test is performed to identify the offline parameters and determine the open-circuit voltage vs. SOC curve. Apart from the standard cycles including Constant Current cycle, Federal Urban Driving Schedule cycle, Urban Dynamometer Driving Schedule cycle and Dynamic Stress Test cycle, a combined cycle is constructed for experimental validation. Furthermore, the study of the effect of sampling time on estimation accuracy and the robustness analysis of the initial value are carried out. The results demonstrate that the proposed method realizes the accurate estimation of SOC with a maximum mean absolute error at 0.50% in five working conditions and shows strong robustness against the sparse sampling and input error.
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Saragih, Naikson Fendier, Surianto Sitepu, Geraldi Titus Simanungkalit, Marzuki Sinambela, Edward Rajagukguk, Frati Gratianus Larosa, and Indra Kelana Jaya. "Validation of CHIRPS Estimation Rainfall Data Using Numerical Accuracy Test with Precitipation Observation Data." IOP Conference Series: Earth and Environmental Science 1083, no. 1 (September 1, 2022): 012095. http://dx.doi.org/10.1088/1755-1315/1083/1/012095.

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Abstract Rainfall is the dominant and most studied weather and climate factor in Indonesia. The use of global satellite estimation data is a solution to overcome the constraints of limited observational rainfall data. Although the global data can be extracted according to the desired location, the data still has to be validated with observational data. This study was conducted to validate the CHIRPS rainfall estimation data with observation rainfall data at the Central MKG Region I Medan. Estimation data used is CHIRPS daily estimation data version 2.0 with a spatial resolution of 0.05°, and validator data is daily observation data of Central MKG Region I Medan for the period 2017- 2019. Validation was done by calculating Pearson correlation, accuracy, bias, mean error (ME), mean absolute error (MAE), and root mean square error (RMSE) values, and using simple linear regression to see overestimated or underestimated estimation data on observation data. Results of this study indicated that the CHIRPS data has a low correlation with the observation data. Large MAE and RMSE values of CHIRPS indicated that the average error of CHIRPS is quite large. Estimation of CHIRPS was underestimated to the observation data so that it is not suitable for daily rainfall forecasting in Medan City. High accuracy value of CHIRPS indicated that CHIRPS was able to detect rain events based on a threshold of 1 mm.
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Correa Alegria, Francisco, and AntÓnio Cruz Serra. "Standard Histogram Test Precision of ADC Gain and Offset Error Estimation." IEEE Transactions on Instrumentation and Measurement 56, no. 5 (October 2007): 1527–31. http://dx.doi.org/10.1109/tim.2007.907978.

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Kambara, Hiroyuki, Keiichi Ohishi, and Yasuharu Koike. "Learning Strategy in Time-to-Contact Estimation of Falling Objects." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 8 (October 20, 2011): 972–79. http://dx.doi.org/10.20965/jaciii.2011.p0972.

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The ability to estimate the time that remains before contact (Time-To-Contact or TTC) of a falling object is critical in daily life. In this paper, we investigated how the Central Nervous System (CNS) becomes able to estimate the TTC of a ball falling at various accelerations. According to experiments on the human ability to catch a ball falling at various accelerations, we assumed that the CNS can hold multiple TTC estimators each of which is trained for a different acceleration, and one of them is adopted for TTC estimation in a ball-catching trial. Here we made a hypothesis about how each TTC estimator is trained when there is an estimation error. (1) If the estimation error is small, the TTC estimator adopted in the trial is recalibrated. (2) If the estimation error is large, a new TTC estimator is created. To test this hypothesis, we conducted two types of ball-catching experiments in a virtual environment where the acceleration of a virtual ball is changed gradually or suddenly in each experiment. The difference in catching performances in the two experiments supported our hypothesis.
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Zhang, Yichong, and Xin Zheng. "Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization." Quantitative Economics 11, no. 3 (2020): 957–82. http://dx.doi.org/10.3982/qe1323.

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In this paper, we study the estimation and inference of the quantile treatment effect under covariate‐adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error underrejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate‐adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.
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Gallagher-Mitchell, Thomas, Victoria Simms, and Damien Litchfield. "Learning from where ‘eye’ remotely look or point: Impact on number line estimation error in adults." Quarterly Journal of Experimental Psychology 71, no. 7 (January 1, 2018): 1526–34. http://dx.doi.org/10.1080/17470218.2017.1335335.

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In this article, we present an investigation into the use of visual cues during number line estimation and their influence on cognitive processes for reducing number line estimation error. Participants completed a 0-1000 number line estimation task before and after a brief intervention in which they observed static-visual or dynamic-visual cues (control, anchor, gaze cursor, mouse cursor) and also made estimation marks to test effective number-target estimation. Results indicated that a significant pre-test to post-test reduction in estimation error was present for dynamic-visual cues of modelled eye-gaze and mouse cursor. However, there was no significant performance difference between pre- and post-test for the control or static anchor conditions. Findings are discussed in relation to the extent to which anchor points alone are meaningful in promoting successful segmentation of the number line and whether dynamic cues promote the utility of these locations in reducing error through attentional guidance.
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Calderon, Sergio, and Daniel Ordoñez Callamad. "Additive Outliers in Open-Loop Threshold Autoregressive Models: A Simulation Study." Revista Colombiana de Estadística 45, no. 1 (January 1, 2022): 1–39. http://dx.doi.org/10.15446/rce.v45n1.92965.

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The effect of additive outliers is studied on an adapted non-linearity test and a robust estimation method for autoregressive coefficients in open-loop TAR (threshold autoregressive) models. Through a Monte Carlo experiment, the power and size of the non-linearity test are studied. Regarding the estimation method, the bias and ratio of mean squared errors are compared between the robust estimator and least squares. Simulation exercises are carried out for different percentages of contamination and the proportion of observations on each model regime. Furthermore, the approximation of the univariate normal distribution to the empirical distribution of estimated coefficients is analyzed along with the coverage level of asymptotic confidence intervals for the parameters. Results show that the adapted non-linearity test does not have size distortions, and it has a superior power than its least-squares counterpart when additive outliers are present. On the other hand, the robust estimation method for the autoregressive coefficients has a better mean squared error than least-squares when this type of observations are present. Lastly, the use of the non-linearity test and the estimation method are illustrated through a real example.
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JIANG, LIANGXIAO, CHAOQUN LI, and ZHIHUA CAI. "DECISION TREE WITH BETTER CLASS PROBABILITY ESTIMATION." International Journal of Pattern Recognition and Artificial Intelligence 23, no. 04 (June 2009): 745–63. http://dx.doi.org/10.1142/s0218001409007296.

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Traditionally, the performance of a classifier is measured by its classification accuracy or error rate. In fact, probability-based classifiers also produce the class probability estimation (the probability that a test instance belongs to the predicted class). This information is often ignored in classification, as long as the class with the highest class probability estimation is identical to the actual class. In many data mining applications, however, classification accuracy and error rate are not enough. For example, in direct marketing, we often need to deploy different promotion strategies to customers with different likelihood (class probability) of buying some products. Thus, accurate class probability estimations are often required to make optimal decisions. In this paper, we firstly review some state-of-the-art probability-based classifiers and empirically investigate their class probability estimation performance. From our experimental results, we can draw a conclusion: C4.4 is an attractive algorithm for class probability estimation. Then, we present a locally weighted version of C4.4 to scale up its class probability estimation performance by combining locally weighted learning with C4.4. We call our improved algorithm locally weighted C4.4, simply LWC4.4. We experimentally test LWC4.4 using the whole 36 UCI data sets selected by Weka. The experimental results show that LWC4.4 significantly outperforms C4.4 in terms of class probability estimation.
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Wang, Yu Ren, Loan T. Q. Ngo, Yi Fan Shih, Yen Ling Lu, and Yi Ming Chen. "Adapting ANNs in SONREB Test to Estimate Concrete Compressive Strength." Key Engineering Materials 792 (December 2018): 166–69. http://dx.doi.org/10.4028/www.scientific.net/kem.792.166.

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SONREB method is a non-destructive testing (NDT) method for estimating the concrete compressive strength. It is conducted by combining two popular NDT methods: ultrasonic pulse velocity (UPV) test and rebound hammer (RH) test. Several researches have been attempted to find the correlation of the different testing method data with actual compressive strength. This research proposes a new Artificial Intelligence based approach, Artificial Neural Networks (ANNs), to estimate the concrete compressive strength using the UPV and RH test data. Data from a total of 315 cylinder concrete samples are collected to develop and validate the ANFIS prediction model. The model prediction results are compared with actual compressive strength using mean absolute percentage error (MAPE). With the adaption of ANFIS, the estimation error of SONREB test can be reduced to 5.98% (measured by MAPE).
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Zheng, Zhiliang. "Load Prediction Model of Athletes’ Physical Training Competition Based on Nonlinear Algorithm Combined with Ultrasound." Contrast Media & Molecular Imaging 2022 (August 24, 2022): 1–7. http://dx.doi.org/10.1155/2022/3465556.

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In order to provide theoretical support and ideas for the “dose” of high-stakes physical activity in athletics, the author has developed models for athletic competition based on nonlinear techniques together with ultrasound. Based on test data, average mean estimation method, and nonlinear regression model estimates, 52 points (46 test points, 6 point estimates) is enrolled in the highest voltage and maximum voltage measurement based on the BP neural network model. The estimation method was developed and the accuracy of the estimation of our estimation method was compared and evaluated using the estimation data. Experimental results show that the average relative error of the average estimate compared to the accuracy of the bench press was 25%, the standard estimate which is not linear regression is 31%, and BP neural network model estimation is 9%. Compared with the accuracy of the assumption of half squatting, the average relative error of the estimated velocity is 13%, the standard nonlinear regression estimate is 20%, and BP neural network model estimated method is 9%. The BP neural network predicts the method with the best performance and intelligence, but its actual functioning and application are complex. The average speed estimate is the most appropriate for use, but the equipment must be high. The process of estimating a linear regression model requires minimal equipment, but its prediction error is high.
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Celik, Nuri. "Robust Post-Hoc Multiple Comparisons: Skew t Distributed Error Terms." Revista Colombiana de Estadística 45, no. 2 (July 14, 2022): 363–72. http://dx.doi.org/10.15446/rce.v45n2.100837.

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The pairwise comparisons or post-hoc methods are used for determining the source of the difference of group means in one-way ANOVA. These methods are mostly depend on normality assumption. However, nonnormal distributions are more prevalent than normal distribution. Therefore, robust estimation methods become very important tools in statistical analysis. In this paper, we assume that the distribution of the error terms is Azzalini's skew $t$ and obtain the robust estimators in order to make post-hoc tests in one-way ANOVA. We use maximum likelihood (ML) methodology and compare this methodology with some of robust estimators like M estimator, Wave estimator, trimmed mean and modified maximum likelihood (MML) methodology with Monte Carlo simulation study. Simulation results show that the proposed methodology is more preferable. We also compare power values of the test statistics and conclude that the test statistics based on the ML estimators are more powerful than the test statistics based on other methods.
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Liu, Yingjie, and Dawei Cui. "Estimation algorithm for vehicle state estimation using ant lion optimization algorithm." Advances in Mechanical Engineering 14, no. 3 (March 2022): 168781322210858. http://dx.doi.org/10.1177/16878132221085839.

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In order to solve the problem of vehicle state estimation, an unscented Kalman filter state parameter estimator based on the Ant lion algorithm is proposed. Aiming at the uncertainty of the noise covariance matrix in the unscented Kalman filter (UKF) process, the Ant lion optimization algorithm (ALO) is used to optimize it. Based on the purpose, a 3-DOF nonlinear vehicle estimation model with Magic formula tire model was established firstly. Then the slalom road operating condition was simulated. The simulation results show that the estimated values of the key state variables are in better agreement with the virtual test values indicating the proposed algorithm having a good estimation performance. And also, compared with the estimation results of the UKF algorithm, the maximum error and the root mean square error of the estimation algorithm proposed in this paper are both smaller than the estimated value of the UKF algorithm. The results of a real-vehicle experiment demonstrate that the proposed method can be used effectively and accurately for solving the vehicle-state estimation problem. The study can provide precise status information for vehicle stability control under extreme conditions.
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Todini, E., F. Pellegrini, and C. Mazzetti. "Influence of parameter estimation uncertainty in Kriging: Part 2 - Test and case study applications." Hydrology and Earth System Sciences 5, no. 2 (June 30, 2001): 225–32. http://dx.doi.org/10.5194/hess-5-225-2001.

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Abstract. The theoretical approach introduced in Part 1 is applied to a numerical example and to the case of yearly average precipitation estimation over the Veneto Region in Italy. The proposed methodology was used to assess the effects of parameter estimation uncertainty on Kriging estimates and on their estimated error variance. The Maximum Likelihood (ML) estimator proposed in Part 1, was applied to the zero mean deviations from yearly average precipitation over the Veneto Region in Italy, obtained after the elimination of a non-linear drift with elevation. Three different semi-variogram models were used, namely the exponential, the Gaussian and the modified spherical, and the relevant biases as well as the increases in variance have been assessed. A numerical example was also conducted to demonstrate how the procedure leads to unbiased estimates of the random functions. One hundred sets of 82 observations were generated by means of the exponential model on the basis of the parameter values identified for the Veneto Region rainfall problem and taken as characterising the true underlining process. The values of parameter and the consequent cross-validation errors, were estimated from each sample. The cross-validation errors were first computed in the classical way and then corrected with the procedure derived in Part 1. Both sets, original and corrected, were then tested, by means of the Likelihood ratio test, against the null hypothesis of deriving from a zero mean process with unknown covariance. The results of the experiment clearly show the effectiveness of the proposed approach. Keywords: yearly rainfall, maximum likelihood, Kriging, parameter estimation uncertainty
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Mao, Zhu, and Michael D. Todd. "Uncertainty Modeling and Quantification for Structural Health Monitoring Features Derived from Frequency Response Estimation." Key Engineering Materials 569-570 (July 2013): 1148–55. http://dx.doi.org/10.4028/www.scientific.net/kem.569-570.1148.

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System identification in the frequency domain plays a fundamental role in many aspects of mechanical and structural engineering. Frequency domain approaches typically involve estimation of a transfer function, whether it is the usual frequency response function (FRF) or an output-to-output transfer model (transmissibility). The field of structural health monitoring, which involves extracting and classifying features mined from in-sit structural performance data for the purposes of damage condition assessment, has exploited many features for this purpose that inherently are derived from estimations of frequency domain models such as the FRF or transmissibility. Structural health monitoring inevitably involves a hypothesis test at the classification stage such as the (common) binary question: are the features mined from data derived from a reference condition or from data derived from a different (test) condition? Inevitably, this decision involves stochastic data, as any such candidate feature is compromised by error, which we categorize as (i) operational and environmental, (ii) measurement, and (iii) computational/estimation. Regardless of source, this noise leads to the propagation of error, resulting in possible false positive (Type I) errors in the classification. As such, the quantification of uncertainty in the estimation of such features is tantamount to making informed decisions based on a hypothesis test. This paper will demonstrate several statistical models that describe the uncertainty in FRF estimation and will compare their performance to features derived from them for the purposes of detecting damage, with ultimate performance evaluated by receiver operating characteristics (ROCs). A simulation and a plate subject to single-input/single-output vibration testing will serve as the comparison testbeds.
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38

Becker, Gilbert. "On the Integrity of Reliability Estimation in Classical Test Theory: The Case for an Additive Coefficient of Stability." Psychological Reports 103, no. 2 (October 2008): 545–65. http://dx.doi.org/10.2466/pr0.103.2.545-565.

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This article addresses deficiencies in the most widely used estimators of reliability and draws attention to the reason that this issue is important. Accurate calibration of relationships between constructs is critical to theory development. Unless workers have accurate estimates of scale reliability, accurate estimates of those relationships will not be forthcoming because the classical disattenuation formula requires them. This article shows that classical test theory can easily accommodate the delineation of its error component E in test scores into two sources, inconsistency across content ( E1) and inconsistency across time ( E2). Viewed from this extended model, the alternate forms approach to reliability estimation is complete in that it gauges simultaneously both sources of error. Because that approach is rarely used today for that purpose, the integrity of estimation has been lost. In its place arose estimators of partial reliability—those for estimating generalizability over one medium or the other, but not both, thereby precluding the additivity of error components. Recent developments promise to restore the integrity of the alternate forms approach without the need for alternate forms and suggest an additive alternative to the current nonadditive coefficient of stability.
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Zhu, Jingbao, Shanyou Li, Qiang Ma, Bin He, and Jindong Song. "Support Vector Machine-Based Rapid Magnitude Estimation Using Transfer Learning for the Sichuan–Yunnan Region, China." Bulletin of the Seismological Society of America 112, no. 2 (February 1, 2022): 894–904. http://dx.doi.org/10.1785/0120210232.

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ABSTRACT The Sichuan–Yunnan region is a seismically active area. To explore the feasibility of using the support vector machine (SVM) method for magnitude estimation in the area and to improve the rapid magnitude estimation accuracy, we construct an SVM magnitude estimation model using transfer learning (TLSVM-M model) based on a single-station record in this study. We find that the magnitude estimation of a single station shows that for the test dataset, within the 3 s time window after the P-wave arrival, the average absolute error (which reflects the size of the estimated magnitude error as a whole) and standard deviation (which reflects the scatter of magnitude estimation error) of the magnitudes estimated by the TLSVM-M model are 0.31 and 0.41, respectively, which are less than those of the SVM magnitude estimation model without transfer learning (0.44 and 0.55, respectively), the τc method (1.35 and 1.74, respectively) and the Pd method (0.44 and 0.56, respectively). In addition, in test involving five earthquake events via the TLSVM-M model, at 1 s after the first station is triggered, the magnitudes of three events (Ms 4.2, 5.2, and 6.3) are estimated within an error range of ±0.3 magnitude units. For the other two earthquakes (Ms 6.6 and 7.0), there is an obvious magnitude underestimation problem at 1 s after the first station is triggered, with less underestimation by increasing time after the first station is triggered. Meanwhile, for these two events (Ms 6.6 and 7.0), within 13 s after the first station was triggered, the magnitude estimation errors are both within ±0.3 magnitude units. The TLSVM-M model has the capability of rapid magnitude estimation for small-to-moderate events in the Sichuan–Yunnan region. Meanwhile, we infer that the proposed model may have potential in earthquake early warning.
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40

Hamza Raheem, Sairan. "Comparison Among Three Estimation Methods to Estimate Cascade Reliability Model (2+1) Based On Inverted Exponential Distribution." Ibn AL- Haitham Journal For Pure and Applied Sciences 33, no. 4 (October 20, 2020): 82. http://dx.doi.org/10.30526/33.4.2512.

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In this paper, we are mainly concerned with estimating cascade reliability model (2+1) based on inverted exponential distribution and comparing among the estimation methods that are used . The maximum likelihood estimator and uniformly minimum variance unbiased estimators are used to get of the strengths and the stress ;k=1,2,3 respectively then, by using the unbiased estimators, we propose Preliminary test single stage shrinkage (PTSSS) estimator when a prior knowledge is available for the scale parameter as initial value due past experiences . The Mean Squared Error [MSE] for the proposed estimator is derived to compare among the methods. Numerical results about conduct of the considered estimator are discussed including the study of mentioned expressions. The numerical results are exhibited and put it in tables.
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41

Zhao, Jinying, Eric Boerwinkle, and Momiao Xiong. "Impact of Haplotype-Frequency Estimation Error on Test Statistics in Association Studies." American Journal of Human Genetics 78, no. 4 (April 2006): 728–29. http://dx.doi.org/10.1086/501074.

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42

Lee, Dongkyu, Sangchul Lee, Sanghyuk Park, and Sangho Ko. "Test and error parameter estimation for MEMS — based low cost IMU calibration." International Journal of Precision Engineering and Manufacturing 12, no. 4 (August 2011): 597–603. http://dx.doi.org/10.1007/s12541-011-0077-9.

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43

Clarke, Judith A. "Preliminary-test estimation of the standard error of estimate in linear regression." Economics Letters 34, no. 1 (September 1990): 27–32. http://dx.doi.org/10.1016/0165-1765(90)90176-2.

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44

Wells, Lucas A., and Woodam Chung. "Evaluation of Ground Plane Detection for Estimating Breast Height in Stereo Images." Forest Science 66, no. 5 (April 9, 2020): 612–22. http://dx.doi.org/10.1093/forsci/fxaa006.

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Abstract Diameter at breast height is a standard method for characterizing trees and ultimately forests over large geographical scales. Expressing the cross-section of a tree stem with a diameter measurement has inherent errors, as stems are not perfect conical frustums. Diameter suffices as an approximation, since methods for the exact cross-sectional area of a stem are infeasible in practice. There are other primary sources of error in diameter at breast height measurements: diameter measurement error and breast height measurement error. This paper addresses the latter in the context of an automated measurement system using 3D photography. We consider breast height estimation a fundamental component in such systems, as errors in measurement height can precipitate significant errors in stand-level attribute estimation as diameter changes along the height of the stem because of taper. We evaluate the efficacy of breast height estimation using stereo photogrammetry by fitting a planar surface to the ground and elevating the plane to breast height. Results from a validation test on 560 observations show that breast height can be estimated with a root mean squared error of 10.20 cm within 10 m from the camera and 13.36 cm within 20 m from the camera on flat terrain in varying levels of stem density. Study Implications Increasing the level of automation in forest operations is one approach to address workforce attrition and safety issues in the industry. Automated tree measurement and mapping systems present an opportunity to reduce operational costs by providing machine operators with necessary information to carry out silvicultural prescriptions and eliminate the need for individual tree marking in certain situations. In order to maintain trust between landowners and harvesting contractors, it is imperative that automatic measurement systems are rigorously tested to determine that measurement accuracy is within acceptable limits. Breast height measurement error is often overlooked as a source of error in estimating diameter at breast height. However, accurate breast height estimation is a necessary prerequisite for reliable, consistent, and precise diameter at breast height measurement. The capacity of machine vision systems to automate forest inventory and monitoring tasks is increasing and can help managers achieve sustainable forestry objectives on more acres in less time.
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Jung, Changbae, and Woojin Chung. "Calibration of Kinematic Parameters for Two Wheel Differential Mobile Robots by Using Experimental Heading Errors." International Journal of Advanced Robotic Systems 8, no. 5 (January 1, 2011): 68. http://dx.doi.org/10.5772/50906.

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Odometry using incremental wheel encoder sensors provides the relative position of mobile robots. This relative position is fundamental information for pose estimation by various sensors for EKF Localization, Monte Carlo Localization etc. Odometry is also used as unique information for localization of environmental conditions when absolute measurement systems are not available. However, odometry suffers from the accumulation of kinematic modeling errors of the wheel as the robot's travel distance increases. Therefore, systematic odometry errors need to be calibrated. Principal systematic error sources are unequal wheel diameters and uncertainty of the effective wheelbase. The UMBmark method is a practical and useful calibration scheme for systematic odometry errors of two-wheel differential mobile robots. However, the approximation errors of the calibration equations and the coupled effect between the two systematic error sources affect the performance of the kinematic parameter estimation. In this paper, we proposed a new calibration scheme whose calibration equations have less approximation errors. This new scheme uses the orientation errors of the robot's final pose in the test track. This scheme also considers the coupled effect between wheel diameter error and wheelbase error. Numerical simulations and experimental results verified that the proposed scheme accurately estimated the kinematic error parameters and improved the accuracy of odometry calibration significantly.
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Xiong, Hao, Dongkai Dai, Yingwei Zhao, Xingshu Wang, Jiaxing Zheng, and Dejun Zhan. "An Analysis of the Attitude Estimation Errors Caused by the Deflections of Vertical in the Integration of Rotational INS and GNSS." Sensors 19, no. 7 (April 10, 2019): 1721. http://dx.doi.org/10.3390/s19071721.

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This paper investigates the attitude estimation errors caused by the deflections of vertical (DOV) in the case of a rotational inertial navigation system (INS) integrated with a global satellite navigation system (GNSS). It has been proved theoretically and experimentally that the DOV can introduce a tilt error to the INS/GNSS integration, whereas less attention has been given to its effect to the heading estimation. In fact, due to the intercoupling characteristic of attitude errors, the heading estimation of an INS/GNSS integrated navigation system can also be affected. In this paper, first, the attitude estimation errors caused by DOV were deduced based on the INS’s error propagation functions. Then, the corresponding simulations were conducted and the results were well consistent with the theoretical analysis. Finally, a real shipborne marine test was organized with the aimed to verify the effect of DOV on attitude estimation in the rotational INS/GNSS integration, whereas the global gravity model was used for DOV compensation. The results with DOV compensation were compared with the corresponding results where the compensation was not used and showed that the heading estimation errors caused by DOV could exceed 20 arcsecs, which must be considered in high-precision application cases.
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Rahman, Haolia, Devi Handaya, and Teguh Budianto. "Estimasi Jumlah Penghuni Ruangan Berdasarkan Konsentrasi CO2 Dengan Metode Bayesian MCMC." Jurnal Rekayasa Mesin 12, no. 1 (May 31, 2021): 125. http://dx.doi.org/10.21776/ub.jrm.2021.012.01.14.

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<span lang="PT-BR">The number of occupants in the building is important information for building management because it is related to security issues, evacuation, and energy saving. This article focuses on estimating the number of occupants using the Bayesian Monte Carlo Markov chain (MCMC) method based on indoor CO<sub>2</sub> levels. Probability theory underlies the Bayesian MCMC principle, where the mass balance equation of indoor CO<sub>2</sub> is used as a physical model of estimation calculations. Determination of the variables in the mass balance equation is investigated to obtain the effect on the accuracy of the estimated number of occupants. It found that the higher the standard deviation of the input variable on the physical model, the higher the error estimation produced. In addition, the Bayesian MCMC algorithm is tested in a real-time scheme of test</span><span lang="IN">-</span><span lang="PT-BR">chamber. The result shows an estimated error of 39%. Rapid changes influence estimation errors in actual occupants relative to the sample interval and the time delay of the estimation.</span>
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48

Murtiyasa, Budi, Afifah Ma'rufi, and Mohd Asrul Affendi bin Abdullah. "Undergraduate students’ errors on interval estimation based on variance neglect." Jurnal Elemen 8, no. 1 (January 6, 2022): 161–74. http://dx.doi.org/10.29408/jel.v8i1.4529.

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Interval estimation is an important topic, especially in drawing conclusions on an event. Mathematics education students must possess the skill to formulate and use interval estimation. The errors of mathematics education students in formulating wrong interval estimates indicate a low understanding of interval estimation. This study explores the errors of mathematics education students in interpreting the variance in the questions regarding selecting the proper test statistic to formulate the interval estimation of mean accurately. Respondents in this study involved 36 students of mathematics education (N = 9 males, N = 27 females). This research is qualitative research with a qualitative descriptive approach. Data collection was carried out using the respondents’ ability test and interviews. The respondents’ ability test instrument was tested on 36 students and declared valid where r-count r-table with r-table of 0.3291, and declared reliable with a Cronbach Alpha value of 0.876 0.6. Through an exploratory approach, data were analyzed by categorizing, reducing, and interpreting to conclude students' abilities and thinking methods in formulating interval estimation of the mean based on the variance in questions. The results showed that mathematics education students neglected the variance, so they could not determine the test statistics correctly, resulting in error interval estimates. This study provides insight into the thinking methods of mathematics education students on variance in interval estimation problems in the hope of anticipating errors in formulating interval estimation problems.
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Guillemot, Gildas, Adrien van Gorp, Thierry Coorevits, and Alain Iost. "Estimation of the Constitutive Law by Dual Small Punch Test and Instrumented Indentation." Solid State Phenomena 188 (May 2012): 193–98. http://dx.doi.org/10.4028/www.scientific.net/ssp.188.193.

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In this paper an inverse finite element procedure was developed to assess the true- stress strain relationship of a DP dual phase. Experiments were performed both by means of instrumented indentation and small punch tests on small samples cut in the same steel sheet. Tests are developed on a Zwick macro-hardness tester. Single test are first proposed in order to estimate the parameters of the constitutive law (K,n). We propose to conduct SPT tests using PTFE lubricant and hard (WC / Co) ball. An inverse method based on the Nelder and Mead algorithm has been developed in order to found experimental curves. Nevertheless we show that this method lead to poor estimation of the parameter of the constitutive law. We propose to improve these estimations by cross-mechanical tests. Indeed we show that the estimation of the low-error (K,n) domains deduced from each single test can be crossed. This method leads to a better estimation of the constitutive law. Moreover both load/displacement curves of SPT and macrohardness can be found again.
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de Oliveira Maciel, Benedito Carlos, Luiz Carlos Sandoval Góes, Elder Moreira Hemerly, and Nei Salis Brasil Neto. "Flight Path Reconstruction and Parameter Estimation Using Output-Error Method." Shock and Vibration 13, no. 4-5 (2006): 379–92. http://dx.doi.org/10.1155/2006/960391.

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This work describes the application of the output-error method using the Levenberg-Marquardt optimization algorithm to the Flight Path Reconstruction (FPR) problem, which constitutes an important preliminary step towards the aircraft parameter identification. This method is also applied to obtain the aerodynamic and control derivatives of a regional jet aircraft from flight test data with measurement noise and bias. Experimental results are reported, employing a real jet aircraft, with flight test data acquired by smart probes, inertial sensors (gyrometers and accelerometers) and Global Positioning Systems (GPS) receivers.
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