Journal articles: 'Local linear estimator'

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Ziegelmann, Flavio A. "NONPARAMETRIC ESTIMATION OF VOLATILITY FUNCTIONS: THE LOCAL EXPONENTIAL ESTIMATOR." Econometric Theory 18, no. 4 (May 17, 2002): 985–91. http://dx.doi.org/10.1017/s026646660218409x.

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Kernel smoothing techniques free the traditional parametric estimators of volatility from the constraints related to their specific models. In this paper the nonparametric local exponential estimator is applied to estimate conditional volatility functions, ensuring its nonnegativity. Its asymptotic properties are established and compared with those for the local linear estimator. It theoretically enables us to determine when the exponential is expected to be superior to the linear estimator. A very strong and novel result is achieved: the exponential estimator is asymptotically fully adaptive to unknown conditional mean functions. Also, our simulation study shows superior performance of the exponential estimator.

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Luo, Shuanghua, Cheng-Yi Zhang, and Fengmin Xu. "The Local LinearM-Estimation with Missing Response Data." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/398082.

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This paper studies the nonparametric regressive function with missing response data. Three local linearM-estimators with the robustness of local linear regression smoothers are presented such that they have the same asymptotic normality and consistency. Then finite-sample performance is examined via simulation studies. Simulations demonstrate that the complete-case dataM-estimator is not superior to the other two local linearM-estimators.

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Zhang, Zhengyu. "LOCAL PARTITIONED QUANTILE REGRESSION." Econometric Theory 33, no. 5 (September 19, 2016): 1081–120. http://dx.doi.org/10.1017/s0266466616000293.

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In this paper, we consider the nonparametric estimation of a broad class of quantile regression models, in which the partially linear, additive, and varying coefficient models are nested. We propose for the model a two-stage kernel-weighted least squares estimator by generalizing the idea of local partitioned mean regression (Christopeit and Hoderlein, 2006, Econometrica 74, 787–817) to a quantile regression framework. The proposed estimator is shown to have desirable asymptotic properties under standard regularity conditions. The new estimator has three advantages relative to existing methods. First, it is structurally simple and widely applicable to the general model as well as its submodels. Second, both the functional coefficients and their derivatives up to any given order can be estimated. Third, the procedure readily extends to censored data, including fixed or random censoring. A Monte Carlo experiment indicates that the proposed estimator performs well in finite samples. An empirical application is also provided.

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Zhu, Hong. "Design and Implementation of Vehicle Self-Navigation System in Urban Intelligent Traffic." Applied Mechanics and Materials 241-244 (December 2012): 2107–10. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.2107.

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Compared with the single sensor measuring, the complementary measuring with the dual sensor can solve some key problems in the vehicle self-navigation system. Two sensors’ data must be fused by the federal state estimator. Based on the Singer model, the system equation of Dead Reckoning sensor is nonlinear and the system equation of Global Positioning System sensor is linear. A two-level estimator is designed and implemented in such a way that two local estimators process the linear and nonlinear systems respectively, and the main estimator fuses the data from two local estimators, so that the optimal global state variables can be estimated. The simulation results show that the two-level estimator of dual sensor can increase the vehicle’s self-navigation precision and can be applied in urban intelligent traffic.

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Kikechi, Conlet Biketi, and Richard Onyino Simwa. "On Comparison of Local Polynomial Regression Estimators for P=0 and P=1 in a Model Based Framework." International Journal of Statistics and Probability 7, no. 4 (June 27, 2018): 104. http://dx.doi.org/10.5539/ijsp.v7n4p104.

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This article discusses the local polynomial regression estimator for and the local polynomial regression estimator for in a finite population. The performance criterion exploited in this study focuses on the efficiency of the finite population total estimators. Further, the discussion explores analytical comparisons between the two estimators with respect to asymptotic relative efficiency. In particular, asymptotic properties of the local polynomial regression estimator of finite population total for are derived in a model based framework. The results of the local polynomial regression estimator for are compared with those of the local polynomial regression estimator for studied by Kikechi et al (2018). Variance comparisons are made using the local polynomial regression estimator for and the local polynomial regression estimator for which indicate that the estimators are asymptotically equivalently efficient. Simulation experiments carried out show that the local polynomial regression estimator outperforms the local polynomial regression estimator in the linear, quadratic and bump populations.

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Casas, Isabel, and Irene Gijbels. "Unstable volatility: the break-preserving local linear estimator." Journal of Nonparametric Statistics 24, no. 4 (December 2012): 883–904. http://dx.doi.org/10.1080/10485252.2012.720981.

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Poměnková, Jitka. "Nonparametric estimate remarks." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 54, no. 3 (2006): 93–100. http://dx.doi.org/10.11118/actaun200654030093.

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Kernel smoothers belong to the most popular nonparametric functional estimates. They provide a simple way of finding structure in data. The idea of the kernel smoothing can be applied to a simple fixed design regression model. This article is focused on kernel smoothing for fixed design regresion model with three types of estimators, the Gasser-Müller estimator, the Nadaraya-Watson estimator and the local linear estimator. At the end of this article figures for ilustration of desribed estimators on simulated and real data sets are shown.

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Li, Degui, Zudi Lu, and Oliver Linton. "LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE: UNIFORM CONSISTENCY WITH CONVERGENCE RATES." Econometric Theory 28, no. 5 (April 27, 2012): 935–58. http://dx.doi.org/10.1017/s0266466612000011.

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Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

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Ziegelmann, Flavio A. "A Local Linear Least-Absolute-Deviations Estimator of Volatility." Communications in Statistics - Simulation and Computation 37, no. 8 (August 27, 2008): 1543–64. http://dx.doi.org/10.1080/03610910802244398.

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Esbati, M., M. A. Khanesar, and A. Shahzadi. "Improving the quality of service in network-based control systems." Transactions of the Institute of Measurement and Control 40, no. 8 (July 24, 2017): 2694–702. http://dx.doi.org/10.1177/0142331217714863.

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The use of data networks in control loops has received much attention recently due to its flexibility and economical advantages. In addition, mutual network usage has raised new challenges such as delay and data loss. This paper aims to reduce undesired effects of network by reducing the required traffic of the network. An estimation framework for network control system is introduced, in which estimations of local Kalman filter is sent to remote estimator based on the logic decided by a novel fuzzy communication logic. In order to do so, there exist two estimators, a remote estimator which estimates the states of the plant and its local copy that gives the same output. The output of the local estimator is compared with the real states of the system, if the states of the system are estimated with small error, there is no need to send data, hence, the probability of sending data is decreased using a fuzzy decision system. In order to optimize this fuzzy system, a particle swarm optimization (PSO) algorithm is used. The proposed method is applied to control a pair of overhead crane systems with non-linear dynamics. Since the two overhead cranes need to work synchronously and their synchronization is performed over a network, the control of this system lies within the scope of the proposed controller. Simulation results show that the communication load is reduced and the purposed fuzzy communication logic is able to control the non-linear dynamical systems over a network with a sufficient performance.

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Hiabu, Munir, María Dolores Martínez-Miranda, Jens Perch Nielsen, Jaap Spreeuw, Carsten Tanggaard, and Andrés M. Villegas. "Global Polynomial Kernel Hazard Estimation." Revista Colombiana de Estadística 38, no. 2 (July 15, 2015): 399–411. http://dx.doi.org/10.15446/rce.v38n2.51668.

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<p>This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically reduces bias with unchanged variance. A simulation study investigates the finite-sample properties of GPA. The method is tested on local constant and local linear estimators. From the simulation experiment we conclude that the global estimator improves the goodness-of-fit. An especially encouraging result is that the bias-correction works well for small samples, where traditional bias reduction methods have a tendency to fail.</p>

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Luo, Shuanghua, Cheng-yi Zhang, and Meihua Wang. "Composite Quantile Regression for Varying Coefficient Models with Response Data Missing at Random." Symmetry 11, no. 9 (August 21, 2019): 1065. http://dx.doi.org/10.3390/sym11091065.

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Composite quantile regression (CQR) estimation and inference are studied for varying coefficient models with response data missing at random. Three estimators including the weighted local linear CQR (WLLCQR) estimator, the nonparametric WLLCQR (NWLLCQR) estimator, and the imputed WLLCQR (IWLLCQR) estimator are proposed for unknown coefficient functions. Under some mild conditions, the proposed estimators are asymptotic normal. Simulation studies demonstrate that the unknown coefficient estimators with IWLLCQR are superior to the other two with WLLCQR and NWLLCQR. Moreover, bootstrap test procedures based on the IWLLCQR fittings is developed to test whether the coefficient functions are actually varying. Finally, a type of investigated real-life data is analyzed to illustrated the applications of the proposed method.

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Liu, Bing, Zhen Chen, Xiangdong Liu, and Fan Yang. "An Efficient Nonlinear Filter for Spacecraft Attitude Estimation." International Journal of Aerospace Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/540235.

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Increasing the computational efficiency of attitude estimation is a critical problem related to modern spacecraft, especially for those with limited computing resources. In this paper, a computationally efficient nonlinear attitude estimation strategy based on the vector observations is proposed. The Rodrigues parameter is chosen as the local error attitude parameter, to maintain the normalization constraint for the quaternion in the global estimator. The proposed attitude estimator is performed in four stages. First, the local attitude estimation error system is described by a polytopic linear model. Then the local error attitude estimator is designed with constant coefficients based on the robustH2filtering algorithm. Subsequently, the attitude predictions and the local error attitude estimations are calculated by a gyro based model and the local error attitude estimator. Finally, the attitude estimations are updated by the predicted attitude with the local error attitude estimations. Since the local error attitude estimator is with constant coefficients, it does not need to calculate the matrix inversion for the filter gain matrix or update the Jacobian matrixes online to obtain the local error attitude estimations. As a result, the computational complexity of the proposed attitude estimator reduces significantly. Simulation results demonstrate the efficiency of the proposed attitude estimation strategy.

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Chan, Nigel, and Qiying Wang. "UNIFORM CONVERGENCE FOR NONPARAMETRIC ESTIMATORS WITH NONSTATIONARY DATA." Econometric Theory 30, no. 5 (April 25, 2014): 1110–33. http://dx.doi.org/10.1017/s026646661400005x.

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Sharp upper and lower uniform bounds are established for a general class of functionals of integrated and fractionally integrated time series. The main result is used to develop optimal uniform convergence for the Nadaraya-Watson estimator and the local linear nonparametric estimator in a nonlinear cointegrating regression model. Unlike the point-wise situation, it is shown that the performance of the local linear nonparametric estimator is superior to that of the Nadaraya-Watson estimator in uniform asymptotics.

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Xu, Ke-Li. "REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS." Econometric Theory 26, no. 2 (September 30, 2009): 541–63. http://dx.doi.org/10.1017/s0266466609100087.

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The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

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Wang, Qiying, and Peter C. B. Phillips. "ASYMPTOTIC THEORY FOR ZERO ENERGY FUNCTIONALS WITH NONPARAMETRIC REGRESSION APPLICATIONS." Econometric Theory 27, no. 2 (August 27, 2010): 235–59. http://dx.doi.org/10.1017/s0266466610000277.

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A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya–Watson estimator has the same limit distribution (to the second order including bias) as the local linear nonparametric estimator.

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Bouezmarni, T., A. El Ghouch, and M. Mesfioui. "Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data." Journal of Probability and Statistics 2011 (2011): 1–16. http://dx.doi.org/10.1155/2011/937574.

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The nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias in the boundary region. Here, we propose new estimators based on the gamma kernels for the density and the hazard rate functions. The estimators are free of bias and achieve the optimal rate of convergence in terms of integrated mean squared error. The mean integrated squared error, the asymptotic normality, and the law of iterated logarithm are studied. A comparison of gamma estimators with the local linear estimator for the density function and with hazard rate estimator proposed by Müller and Wang (1994), which are free from boundary bias, is investigated by simulations.

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Cai, Zongwu. "REGRESSION QUANTILES FOR TIME SERIES." Econometric Theory 18, no. 1 (February 2002): 169–92. http://dx.doi.org/10.1017/s0266466602181096.

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In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for α-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, variance, and, more important, automatic good boundary behavior properties of local linear “double-kernel” estimators introduced by Yu and Jones (1998, Journal of the American Statistical Association 93, 228–237), but also has the additional advantage of always being a distribution itself. Second, it is shown that under some regularity conditions, the WNW conditional quantile estimator is weakly consistent and normally distributed and that it inherits all good properties from the WNW conditional distribution estimator. A small simulation study is carried out to illustrate the performance of the estimates, and a real example is also used to demonstrate the methodology.

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Zhang, Lili, and Jangsun Baek. "The local influence of LIU type estimator in linear mixed model." Journal of the Korean Data and Information Science Society 26, no. 2 (March 31, 2015): 465–74. http://dx.doi.org/10.7465/jkdi.2015.26.2.465.

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Puspitawati, A., and N. Chamidah. "Choroidal Neovascularisation Classification on Fundus Retinal Images Using Local Linear Estimator." IOP Conference Series: Materials Science and Engineering 546 (June 26, 2019): 052056. http://dx.doi.org/10.1088/1757-899x/546/5/052056.

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Nguyen, Danh V., and Damla Şentürk. "A consistent local linear estimator of the covariate adjusted correlation coefficient." Statistics & Probability Letters 79, no. 15 (August 2009): 1684–89. http://dx.doi.org/10.1016/j.spl.2009.04.021.

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Zhao, Wen-Xiao, Wei Xing Zheng, and Er-Wei Bai. "A Recursive Local Linear Estimator for Identification of Nonlinear ARX Systems*." IFAC Proceedings Volumes 45, no. 16 (July 2012): 1517–22. http://dx.doi.org/10.3182/20120711-3-be-2027.00211.

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Sun, Xiao Jun. "Globally Optimal Weighted Fusion White Noise Deconvolution Estimator." Advanced Materials Research 823 (October 2013): 422–27. http://dx.doi.org/10.4028/www.scientific.net/amr.823.422.

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White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. A globally optimal weighted fusion white noise deconvolution estimator is presented for the multisensor linear discrete systems using the Kalman filtering method. It is derived from the centralized fusion white noise deconvolution estimator so that it is identical to the centralized fuser, i.e. it has the global optimality. Compared with the existing globally suboptimal distributed fusion white noise estimators, the proposed white noise fuser is given based on the local Kalman predictors, and the computation of complex covariance matrices is avoided. A simulation for the Bernoulli-Gaussian input white noise shows the effectiveness of the proposed results.

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Khardani, Salah, and Abdelkader Benkhaled. "A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach." Mathematica Slovaca 71, no. 2 (April 1, 2021): 429–38. http://dx.doi.org/10.1515/ms-2017-0479.

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Abstract In this paper, we investigate the problem of the local linear estimation of the conditional ageing intensity function, when the variable of interest is subject to random right-censored. We establish under appropriate conditions the asymptotic normality of this estimator.

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Wang, Xin, Zhi Yu, Le Yang, and Ji Li. "Design and Analysis of a Non-Iterative Estimator for Target Location in Multistatic Sonar Systems with Sensor Position Uncertainties." Mathematics 8, no. 1 (January 15, 2020): 129. http://dx.doi.org/10.3390/math8010129.

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Target location is the basic application of a multistatic sonar system. Determining the position/velocity vector of a target from the related sonar observations is a nonlinear estimation problem. The presence of possible sensor position uncertainties turns this problem into a more challenging hybrid parameter estimation problem. Conventional gradient-based iterative estimators suffer from the problems of initialization difficulties and local convergence. Even if there is no problem with initialization and convergence, a large computational cost is required in most cases. In view of these drawbacks, we develop a computationally efficient non-iterative position/velocity estimator. The main numerical computation involved is the weighted least squares optimization, which makes the estimator computationally efficient. Parameter transformation, model linearization and two-stage processing are exploited to prevent the estimator from iterative computation. Through performance analysis and experimental verification, we find that the proposed estimator reaches the hybrid Cramér–Rao bound and has linear computational complexity.

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Mahmoud, Hamdy F. F. "Parametric Versus Semi and Nonparametric Regression Models." International Journal of Statistics and Probability 10, no. 2 (February 23, 2021): 90. http://dx.doi.org/10.5539/ijsp.v10n2p90.

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There are three common types of regression models: parametric, semiparametric and nonparametric regression. The model should be used to fit the real data depends on how much information is available about the form of the relationship between the response variable and explanatory variables, and the random error distribution that is assumed. Researchers need to be familiar with each modeling approach requirements. In this paper, differences between these models, common estimation methods, robust estimation, and applications are introduced. For parametric models, there are many known methods of estimation, such as least squares and maximum likelihood methods which are extensively studied but they require strong assumptions. On the other hand, nonparametric regression models are free of assumptions regarding the form of the response-explanatory variables relationships but estimation methods, such as kernel and spline smoothing are computationally expensive and smoothing parameters need to be obtained. For kernel smoothing there two common estimators: local constant and local linear smoothing methods. In terms of bias, especially at the boundaries of the data range, local linear is better than local constant estimator.  Robust estimation methods for linear models are well studied, however the robust estimation methods in nonparametric regression methods are limited. A robust estimation method for the semiparametric and nonparametric regression models is introduced.

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Duan, X. L., Z. M. Qian, and W. A. Zheng. "On Local Linear Approximations to Diffusion Processes." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–26. http://dx.doi.org/10.1155/2011/906846.

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Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hence it is difficult to derive the exact maximum likelihood estimator (MLE). There are many different approaches proposed by various authors over the past years, see, for example, the excellent books and Kutoyants (2004), Liptser and Shiryayev (1977), Kushner and Dupuis (2002), and Prakasa Rao (1999), and also the recent works by Aït-Sahalia (1999), (2004), (2002), and so forth. Shoji and Ozaki (1998; see also Shoji and Ozaki (1995) and Shoji and Ozaki (1997)) proposed a simple local linear approximation. In this paper, among other things, we show that Shoji's local linear Gaussian approximation indeed yields a good MLE.

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Benkhaled, Abdelkader, Fethi Madani, and Salah Khardani. "Strong consistency of local linear estimation of a conditional density function under random censorship." Arabian Journal of Mathematics 9, no. 3 (May 16, 2020): 513–29. http://dx.doi.org/10.1007/s40065-020-00282-1.

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Abstract In this paper, we study nonparametric local linear estimation of the conditional density of a randomly censored scalar response variable given a functional random covariate. We establish under general conditions the pointwise almost sure convergence with rates of this estimator under $$\alpha $$ α -mixing dependence. Finally, to show interests of our results, on the practical point of view, we have conducted a computational study, first on a simulated data and, then on some real data concerning Kidney transplant data.

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Żychaluk, K. "Bootstrap bandwidth selection method for local linear estimator in exponential family models." Journal of Nonparametric Statistics 26, no. 2 (March 10, 2014): 305–19. http://dx.doi.org/10.1080/10485252.2014.885023.

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Bâ, Diam, Cheikh Tidiane Seck, and Gane Samb Lô. "Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator." Applied Mathematics 06, no. 12 (2015): 2077–95. http://dx.doi.org/10.4236/am.2015.612183.

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Kaji, Tetsuya. "Theory of Weak Identification in Semiparametric Models." Econometrica 89, no. 2 (2021): 733–63. http://dx.doi.org/10.3982/ecta16413.

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We provide general formulation of weak identification in semiparametric models and an efficiency concept. Weak identification occurs when a parameter is weakly regular, that is, when it is locally homogeneous of degree zero. When this happens, consistent or equivariant estimation is shown to be impossible. We then show that there exists an underlying regular parameter that fully characterizes the weakly regular parameter. While this parameter is not unique, concepts of sufficiency and minimality help pin down a desirable one. If estimation of minimal sufficient underlying parameters is inefficient, it introduces noise in the corresponding estimation of weakly regular parameters, whence we can improve the estimators by local asymptotic Rao–Blackwellization. We call an estimator weakly efficient if it does not admit such improvement. New weakly efficient estimators are presented in linear IV and nonlinear regression models. Simulation of a linear IV model demonstrates how 2SLS and optimal IV estimators are improved.

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Fangfang, Peng, and Sun Shuli. "Distributed Fusion Estimation for Multisensor Multirate Systems with Stochastic Observation Multiplicative Noises." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/373270.

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This paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises. The dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update period. Moreover, different sensors have the different sampling rates and observations of sensors are subject to the stochastic uncertainties of multiplicative noises. At first, local filters at the observation sampling points are obtained based on the observations of each sensor. Further, local estimators at the state update points are obtained by predictions of local filters at the observation sampling points. They have the reduced computational cost and a good real-time property. Then, the cross-covariance matrices between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators and the cross-covariance matrices. An example shows the effectiveness of the proposed algorithms.

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Xiong, Qiang, Yuan Li, and XingFa Zhang. "The Profile Likelihood Estimation for Single-Index ARCH(p)-M Model." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/189426.

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We propose a class of single-index ARCH(p)-M models and investigate estimators of the parametric and nonparametric components. We first estimate the nonparametric component using local linear smoothing technique and then construct an estimator of parametric component by using profile quasimaximum likelihood method. Under regularity conditions, the asymptotic properties of our estimators are established.

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Zhang, Peng, Wen Juan Qi, and Zi Li Deng. "Covariance Intersection Fusion Kalman Estimator for Multi-Sensor System with Measurements Delays." Applied Mechanics and Materials 475-476 (December 2013): 460–65. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.460.

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To handle the state estimation fusion problem between local estimation errors for the system with unknown cross-covariances and to avoid a large computation complexity of cross-covariances, for a multi-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained, and then using the covariance intersection (CI) fusion method, the covariance intersection fusion steady-state Kalman estimator is presented. It is proved that its accuracy is higher than that of each local estimator, and is lower than that of optimal Kalman fuser weighted by matrices with known cross-covariances. A Monte-Carlo simulation example shows the above accuracy relations, hence it has good performances.

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Li, Hua, and Jie Zhou. "Minimax Robust Optimal Estimation Fusion for Distributed Multisensor Systems with a Relative Entropy Uncertainty." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/910971.

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This paper considers the robust estimation fusion problem for distributed multisensor systems with uncertain correlations of local estimation errors. For an uncertain class characterized by the Kullback-Leibler (KL) divergence from the actual model to nominal model of local estimation error covariance, the robust estimation fusion problem is formulated to find a linear minimum variance unbiased estimator for the least favorable model. It is proved that the optimal fuser under nominal correlation model is robust while the estimation error has a relative entropy uncertainty.

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Lin, ZhengYan, YuPing Song, and JiangSheng Yi. "Local linear estimator for stochastic differential equations driven by α-stable Lévy motions." Science China Mathematics 57, no. 3 (December 30, 2013): 609–26. http://dx.doi.org/10.1007/s11425-013-4628-7.

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Zhang, Liang, Bin Zhang, Cong Liu, and Yixue Chen. "Analysis of Spatial Discretization Error Estimators Implemented in ARES Transport Code for SN Equations." Science and Technology of Nuclear Installations 2018 (July 9, 2018): 1–10. http://dx.doi.org/10.1155/2018/3965309.

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The discrete ordinates method (SN) is one of the mainstream methods for neutral particle transport calculations. Assessing the quality of the numerical solution and controlling the discrete error are essential parts of large-scale high-fidelity simulations of nuclear systems. Three error estimators, a two-mesh estimator, a residual-based estimator, and a dual-weighted residual estimator, are derived and implemented in the ARES transport code to evaluate the error of zeroth-order spatial discretization for SN equations. The difference in scalar fluxes on coarse and fine meshes is adopted to indicate the error in the two-mesh method. To avoid zero residual in zeroth-order discretization, angular fluxes within one cell are reconstructed by Legendre polynomials. The error is estimated by inverting the discrete transport operator using the estimated directional residual as an anisotropic source. The inner product of the forward directional residual and the adjoint angular flux is employed to quantify the error in quantities of interest which can be denoted by a linear functional of forward angular flux. Method of Manufactured Solutions (MMS) is adopted to generate analytical solutions for SN equation with scattering and the determined true error is used to evaluate the effectivity of these estimators. Promising results are obtained in the numerical results for both homogeneous and heterogeneous cases. The larger error region is well captured and the average effectivity index for the local error estimation is less than unity. For the series test problems, the estimated goal quantity error can be contained within an order of magnitude around the exact error.

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Cui, Shitong, Le Liu, Wei Xing, and Xudong Zhao. "Periodic Event-Triggered Estimation for Networked Control Systems." Electronics 10, no. 18 (September 10, 2021): 2215. http://dx.doi.org/10.3390/electronics10182215.

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This paper considers the problem of remote state estimation in a linear discrete invariant system, where a smart sensor is utilized to measure the system state and generate a local estimate. The communication depends on an event scheduler in the smart sensor. When the channel between the remote estimator and the smart sensor is activated, the remote estimator simply adopts the estimate transmitted by the smart sensor. Otherwise, it calculates an estimate based on the available information. The closed-form of the minimum mean-square error (MMSE) estimator is introduced, and we use Gaussian preserving event-based sensor scheduling to obtain an ideal compromise between the communication cost and estimation quality. Furthermore, we calculate a variation range of communication probability, which helps to design the policy of event-triggered estimation. Finally, the simulation results are given to illustrate the effectiveness of the proposed event-triggered estimator.

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Peng, Liang, and Shan Sun. "Comparisons Between Local Linear Estimator and Kernel Smooth Estimator for a Smooth Distribution Based on MSE Under Right Censoring." Communications in Statistics - Theory and Methods 36, no. 2 (February 6, 2007): 297–312. http://dx.doi.org/10.1080/03610920600974351.

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Hansen, Bruce E. "AVERAGING ESTIMATORS FOR REGRESSIONS WITH A POSSIBLE STRUCTURAL BREAK." Econometric Theory 25, no. 6 (December 2009): 1498–514. http://dx.doi.org/10.1017/s0266466609990235.

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This paper investigates selection and averaging of linear regressions with a possible structural break. Our main contribution is the construction of a Mallows criterion for the structural break model. We show that the correct penalty term is nonstandard and depends on unknown parameters, but it can be approximated by an average of limiting cases to yield a feasible penalty with good performance. Following Hansen (2007, Econometrica 75, 1175–1189) we recommend averaging the structural break estimates with the no-break estimates where the weight is selected to minimize the Mallows criterion. This estimator is simple to compute, as the weights are a simple function of the ratio of the penalty to the Andrews SupF test statistic.To assess performance we focus on asymptotic mean-squared error (AMSE) in a local asymptotic framework. We show that the AMSE of the estimators depends exclusively on the parameter variation function. Numerical comparisons show that the unrestricted least-squares and pretest estimators have very large AMSE for certain regions of the parameter space, whereas our averaging estimator has AMSE close to the infeasible optimum.

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Zhao, Jian-Qiang, Yan-Yong Zhao, Jin-Guan Lin, Zhang-Xiao Miao, and Waled Khaled. "Estimation and testing for panel data partially linear single-index models with errors correlated in space and time." Random Matrices: Theory and Applications 09, no. 02 (November 7, 2019): 2150005. http://dx.doi.org/10.1142/s2010326321500052.

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We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.

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Chamidah, Nur, Yolanda Swastika Yonani, Elly Ana, and Budi Lestari. "Identification the number of Mycobacterium tuberculosis based on sputum image using local linear estimator." Bulletin of Electrical Engineering and Informatics 9, no. 5 (October 1, 2020): 2109–16. http://dx.doi.org/10.11591/eei.v9i5.2021.

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Infectious disease caused by infection of Mycobacterium tuberculosis is called tuberculosis (TB). A common method in detecting TB is by identifying number of mycobacterium TB in sputum manually. Unfortunately, manually calculation by pathologists take a relatively long time. Previous researches on TB bacteria were still limited to detect the absence or presence of mycobacterium TB in images of sputum. This research aims are identifying number of mycobacterium TB and determining accuracy of classification TB severity by approaching nonparametric Poisson regression model and applying an estimator namely local linear. Steps include processing of image, reducing of dimension by applying partial least square and discrete wavelet transformation, and then identifying the number of mycobacterium TB by using the proposed model approach. In this research, we get deviance values of 28.410 for nonparametric and 93.029 for parametric approaches and the average of classification accuracy values for 4 iterations of 92.75% for nonparametric and 85.5% for parametric approaches. Thus, for identifying many of mycobacterium TB met in images of sputum and classifying of TB severity, the proposed identifying method gives higher accuracy and shorter time in identifying number of mycobacterium TB than parametric linear regression method.

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Chamidah, N., E. Tjahjono, A. R. Fadilah, and B. Lestari. "Standard Growth Charts for Weight of Children in East Java Using Local Linear Estimator." Journal of Physics: Conference Series 1097 (September 2018): 012092. http://dx.doi.org/10.1088/1742-6596/1097/1/012092.

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Butusov, Denis. "Adaptive Stepsize Control for Extrapolation Semi-Implicit Multistep ODE Solvers." Mathematics 9, no. 9 (April 23, 2021): 950. http://dx.doi.org/10.3390/math9090950.

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Developing new and efficient numerical integration techniques is of great importance in applied mathematics and computer science. Among the variety of available methods, multistep ODE solvers are broadly used in simulation software. Recently, semi-implicit integration proved to be an efficient compromise between implicit and explicit ODE solvers, and multiple high-performance semi-implicit methods were proposed. However, the computational efficiency of any ODE solver can be significantly increased through the introduction of an adaptive integration stepsize, but it requires the estimation of local truncation error. It is known that recently proposed extrapolation semi-implicit multistep methods (ESIMM) cannot operate with existing local truncation error (LTE) estimators, e.g., embedded methods approach, due to their specific right-hand side calculation algorithm. In this paper, we propose two different techniques for local truncation error estimation and study the performance of ESIMM methods with adaptive stepsize control. The first considered approach is based on two parallel semi-implicit solutions with different commutation orders. The second estimator, called the “double extrapolation” method, is a modification of the embedded method approach. The introduction of the double extrapolation LTE estimator allowed us to additionally increase the precision of the ESIMM solver. Using several known nonlinear systems, including stiff van der Pol oscillator, as the testbench, we explicitly show that ESIMM solvers can outperform both implicit and explicit linear multistep methods when implemented with an adaptive stepsize.

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Carstensen, Carsten, and Martin Eigel. "Reliable Averaging for the Primal Variable in the Courant FEM and Hierarchical Error Estimators on Red-Refined Meshes." Computational Methods in Applied Mathematics 16, no. 2 (April 1, 2016): 213–30. http://dx.doi.org/10.1515/cmam-2016-0010.

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AbstractA hierarchical a posteriori error estimator for the first-order finite element method (FEM) on a red-refined triangular mesh is presented for the 2D Poisson model problem. Reliability and efficiency with some explicit constant is proved for triangulations with inner angles smaller than or equal to ${\frac{\pi }{2}}$. The error estimator does not rely on any saturation assumption and is valid even in the pre-asymptotic regime on arbitrarily coarse meshes. The evaluation of the estimator is a simple post-processing of the piecewise linear FEM without any extra solve plus a higher-order approximation term. The results also allow the striking observation that arbitrary local averaging of the primal variable leads to a reliable and efficient error estimation. Several numerical experiments illustrate the performance of the proposed a posteriori error estimator for computational benchmarks.

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Nidhomuddin, N. Chamidah, and A. Kurniawan. "Estimation of Biresponse Multipredictor Model using Local Linear Estimator in Case of Scholastic Aptitude and Islamic Tests Modeling." Journal of Physics: Conference Series 1764, no. 1 (February 1, 2021): 012076. http://dx.doi.org/10.1088/1742-6596/1764/1/012076.

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Guo, Hailong, Cong Xie, and Ren Zhao. "Superconvergent gradient recovery for virtual element methods." Mathematical Models and Methods in Applied Sciences 29, no. 11 (October 2019): 2007–31. http://dx.doi.org/10.1142/s0218202519500386.

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Virtual element method is a new promising finite element method using general polygonal meshes. Its optimal a priori error estimates are well established in the literature. In this paper, we take a different viewpoint. We try to uncover the superconvergent property of virtual element methods by doing some local post-processing only on the degrees of freedom. Using the linear virtual element method as an example, we propose a universal gradient recovery procedure to improve the accuracy of gradient approximation for numerical methods using general polygonal meshes. Its capability of serving as a posteriori error estimators in adaptive computation is also investigated. Compared to the existing residual-type a posteriori error estimators for the virtual element methods, the recovery-type a posteriori error estimator based on the proposed gradient recovery technique is much simpler in implementation and it is asymptotically exact. A series of benchmark tests are presented to numerically illustrate the superconvergence of recovered gradient and validate the asymptotic exactness of the recovery-based a posteriori error estimator.

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Todorov, Emanuel. "Stochastic Optimal Control and Estimation Methods Adapted to the Noise Characteristics of the Sensorimotor System." Neural Computation 17, no. 5 (May 1, 2005): 1084–108. http://dx.doi.org/10.1162/0899766053491887.

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Optimality principles of biological movement are conceptually appealing and straightforward to formulate. Testing them empirically, however, requires the solution to stochastic optimal control and estimation problems for reasonably realistic models of the motor task and the sensorimotor periphery. Recent studies have highlighted the importance of incorporating biologically plausible noise into such models. Here we extend the linear-quadratic-gaussian framework—currently the only framework where such problems can be solved efficiently—to include control-dependent, state-dependent, and internal noise. Under this extended noise model, we derive a coordinate-descent algorithm guaranteed to converge to a feedback control law and a nonadaptive linear estimator optimal with respect to each other. Numerical simulations indicate that convergence is exponential, local minima do not exist, and the restriction to nonadaptive linear estimators has negligible effects in the control problems of interest. The application of the algorithm is illustrated in the context of reaching movements. A Matlab implementation is available at www.cogsci.ucsd.edu/∼todorov .

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Dörsek, Philipp, and Jens M. Melenk. "Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEM in Nearly Incompressible Linear Elasticity." Computational Methods in Applied Mathematics 13, no. 3 (July 1, 2013): 291–304. http://dx.doi.org/10.1515/cmam-2013-0007.

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Abstract. We consider the extension of the p-robust equilibrated error estimator due to Braess, Pillwein and Schöberl to linear elasticity. We derive a formulation where the local mixed auxiliary problems do not require symmetry of the stresses. The resulting error estimator is p-robust, and the reliability estimate is also robust in the incompressible limit if quadratics are included in the approximation space. Extensions to other systems of linear second-order partial differential equations are discussed. Numerical simulations show only moderate deterioration of the effectivity index for a Poisson ratio close to .

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Grasse, D. W., and K. A. Moxon. "Correcting the Bias of Spike Field Coherence Estimators Due to a Finite Number of Spikes." Journal of Neurophysiology 104, no. 1 (July 2010): 548–58. http://dx.doi.org/10.1152/jn.00610.2009.

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The coherence between oscillatory activity in local field potentials (LFPs) and single neuron action potentials, or spikes, has been suggested as a neural substrate for the representation of information. The power spectrum of a spike-triggered average (STA) is commonly used to estimate spike field coherence (SFC). However, when a finite number of spikes is used to construct the STA, the coherence estimator is biased. We introduce here a correction for the bias imposed by the limited number of spikes available in experimental conditions. In addition, we present an alternative method for estimating SFC from an STA by using a filter bank approach. This method is shown to be more appropriate in some analyses, such as comparing coherence across frequency bands. The proposed bias correction is a linear transformation derived from an idealized model of spike–field interaction but is shown to hold in more realistic settings. Uncorrected and corrected SFC estimates from both estimation methods are compared across multiple simulated spike–field models and experimentally collected data. The bias correction was shown to reduce the bias of the estimators, but add variance. However, the corrected estimates had a reduced or unchanged mean squared error in the majority of conditions evaluated. The bias correction provides an effective way to reduce bias in an SFC estimator without increasing the mean squared error.

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Journal articles on the topic 'Local linear estimator'

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