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Artykuły w czasopismach na temat "Minimum residual sum of squares"
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Zhou, Zhen, L. N. Zhang, Y. Qin, D. Z. Ma, and B. Niu. "Statistical Inference of LZL-Type Mass Flowmeter Life Distribution Model." Key Engineering Materials 458 (December 2010): 173–78. http://dx.doi.org/10.4028/www.scientific.net/kem.458.173.
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Characteristics of field failure data are analyzed in this paper. The failure data and sales record of LZL-type mass flowmeter are used to infer life distribution of this conduct. The lines can be fitted in coordinates of six distribution using least square and the residual sum of squares are compared, the minimum correspond is the best distribution type. The results show that the life distribution style of this conduct is the two parameter exponential distribution, which is the base to analyze and predict failure development, research failure mechanism and draw up maintenance policy.
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DEVITA, HANY, I. KOMANG GDE SUKARSA, and I. PUTU EKA N. KENCANA. "KINERJA JACKKNIFE RIDGE REGRESSION DALAM MENGATASI MULTIKOLINEARITAS." E-Jurnal Matematika 3, no. 4 (2014): 146. http://dx.doi.org/10.24843/mtk.2014.v03.i04.p077.
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Ordinary least square is a parameter estimations for minimizing residual sum of squares. If the multicollinearity was found in the data, unbias estimator with minimum variance could not be reached. Multicollinearity is a linear correlation between independent variabels in model. Jackknife Ridge Regression(JRR) as an extension of Generalized Ridge Regression (GRR) for solving multicollinearity. Generalized Ridge Regression is used to overcome the bias of estimators caused of presents multicollinearity by adding different bias parameter for each independent variabel in least square equation after transforming the data into an orthoghonal form. Beside that, JRR can reduce the bias of the ridge estimator. The result showed that JRR model out performs GRR model.
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Araveeporn, Autcha. "Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method." Mathematics 8, no. 1 (2020): 62. http://dx.doi.org/10.3390/math8010062.
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This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.
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Liu, Kexin, Weimin Bao, Yufeng Hu, et al. "Improvement in Ridge Coefficient Optimization Criterion for Ridge Estimation-Based Dynamic System Response Curve Method in Flood Forecasting." Water 13, no. 24 (2021): 3483. http://dx.doi.org/10.3390/w13243483.
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The ridge estimation-based dynamic system response curve (DSRC-R) method, which is an improvement of the dynamic system response curve (DSRC) method via the ridge estimation method, has illustrated its good robustness. However, the optimization criterion for the ridge coefficient in the DSRC-R method still needs further study. In view of this, a new optimization criterion called the balance and random degree criterion considering the sum of squares of flow errors (BSR) is proposed in this paper according to the properties of model-simulated residuals. In this criterion, two indexes, namely, the random degree of simulated residuals and the balance degree of simulated residuals, are introduced to describe the independence and the zero mean property of simulated residuals, respectively. Therefore, the BSR criterion is constructed by combining the sum of squares of flow errors with the two indexes. The BSR criterion, L-curve criterion and the minimum sum of squares of flow errors (MSSFE) criterion are tested on both synthetic cases and real-data cases. The results show that the BSR criterion is better than the L-curve criterion in minimizing the sum of squares of flow residuals and increasing the ridge coefficient optimization speed. Moreover, the BSR criterion has an advantage over the MSSFE criterion in making the estimated rainfall error more stable.
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Marjetič, Aleš. "Least-squares adjustment taking into account the errors in variables." Geodetski vestnik 65, no. 02 (2021): 205–18. http://dx.doi.org/10.15292/geodetski-vestnik.2021.02.205-218.
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In this article, we discuss the procedure for computing the values of the unknowns under the condition of the minimum sum of squares of the observation residuals (least-squares method), taking into account the errors in the unknowns. Many authors have already presented the problem, especially in the field of regression analysis and computations of transformation parameters. We present an overview of the theoretical foundations of the least-squares method and extensions of this method by considering the errors in unknowns in the model matrix. The method, which can be called ‘the total least-squares method’, is presented in the paper for the case of fitting the regression line to a set of points and for the case of calculating transformation parameters for the transition between the old and the new Slovenian national coordinate systems. With the results based on relevant statistics, we confirm the suitability of the considered method for solving such tasks.
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Pizarro Inostroza, María Gabriela, Francisco Javier Navas González, Vincenzo Landi, et al. "Goat Milk Nutritional Quality Software-Automatized Individual Curve Model Fitting, Shape Parameters Calculation and Bayesian Flexibility Criteria Comparison." Animals 10, no. 9 (2020): 1693. http://dx.doi.org/10.3390/ani10091693.
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SPSS syntax was described to evaluate the individual performance of 49 linear and non-linear models to fit the milk component evolution curve of 159 Murciano-Granadina does selected for genotyping analyses. Peak and persistence for protein, fat, dry matter, lactose, and somatic cell counts were evaluated using 3107 controls (3.91 ± 2.01 average lactations/goat). Best-fit (adjusted R2) values (0.548, 0.374, 0.429, and 0.624 for protein, fat, dry matter, and lactose content, respectively) were reached by the five-parameter logarithmic model of Ali and Schaeffer (ALISCH), and for the three-parameter model of parabolic yield-density (PARYLDENS) for somatic cell counts (0.481). Cross-validation was performed using the Minimum Mean-Square Error (MMSE). Model comparison was performed using Residual Sum of Squares (RSS), Mean-Squared Prediction Error (MSPE), adjusted R2 and its standard deviation (SD), Akaike (AIC), corrected Akaike (AICc), and Bayesian information criteria (BIC). The adjusted R2 SD across individuals was around 0.2 for all models. Thirty-nine models successfully fitted the individual lactation curve for all components. Parametric and computational complexity promote variability-capturing properties, while model flexibility does not significantly (p > 0.05) improve the predictive and explanatory potential. Conclusively, ALISCH and PARYLDENS can be used to study goat milk composition genetic variability as trustable evaluation models to face future challenges of the goat dairy industry.
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UTAMI, NI KETUT TRI, and I. KOMANG GDE SUKARSA. "PENERAPAN METODE GENERALIZED RIDGE REGRESSION DALAM MENGATASI MASALAH MULTIKOLINEARITAS." E-Jurnal Matematika 2, no. 1 (2013): 54. http://dx.doi.org/10.24843/mtk.2013.v02.i01.p029.
Pełny tekst źródłaStreszczenie:
Ordinary least square is parameter estimation method for linier regression analysis by minimizing residual sum of square. In the presence of multicollinearity, estimators which are unbiased and have a minimum variance can not be generated. Multicollinearity refers to a situation where regressor variables are highly correlated. Generalized Ridge Regression is an alternative method to deal with multicollinearity problem. In Generalized Ridge Regression, different biasing parameters for each regressor variables were added to the least square equation after transform the data to the space of orthogonal regressors. The analysis showed that Generalized Ridge Regression was satisfactory to overcome multicollinearity.
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Annan, Richard Fiifi, Yao Yevenyo Ziggah, John Ayer, and Christian Amans Odutola. "ACCURACY ASSESSMENT OF HEIGHTS OBTAINED FROM TOTAL STATION AND LEVEL INSTRUMENT USING TOTAL LEAST SQUARES AND ORDINARY LEAST SQUARES METHODS." Geoplanning: Journal of Geomatics and Planning 3, no. 2 (2016): 87. http://dx.doi.org/10.14710/geoplanning.3.2.87-92.
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Spirit levelling has been the traditional means of determining Reduced Levels (RL’s) of points by most surveyors. The assertion that the level instrument is the best instrument for determining elevations of points needs to be reviewed; this is because technological advancement is making the total station a very reliable tool for determining reduced levels of points. In order to achieve the objective of this research, reduced levels of stations were determined by a spirit level and a total station instrument. Ordinary Least Squares (OLS) and Total Least Squares (TLS) techniques were then applied to adjust the level network. Unlike OLS which considers errors only in the observation matrix, and adjusts observations in order to make the sum of its residuals minimum, TLS considers errors in both the observation matrix and the data matrix, thereby minimising the errors in both matrices. This was evident from the results obtained in this study such that OLS approximated the adjusted reduced levels, which compromises accuracy, whereas the opposite happened in the TLS adjustment results. Therefore, TLS was preferred to OLS and Analysis of Variance (ANOVA) was performed on the preferred TLS solution and the RL’s from the total station in order to ascertain how accurate the total station can be relative to the spirit level.
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Zverev, S. V., V. I. Karpov, and M. A. Nikitina. "Optimization of food compositions according to the ideal protein profile." Food systems 4, no. 1 (2021): 4–11. http://dx.doi.org/10.21323/2618-9771-2021-4-1-4-11.
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The paper emphasizes the importance of not only the quantitative but also qualitative composition of protein in nutrition. The authors propose protein classification into three main groups according to the concept of reference (ideal) protein. A mathematical model is examined to solve the task of rational mixture production upon the given profile of reference protein. Two variants of the criterion for formation of optimal composition are described. One of them presents the classical sum of squares of the residual for essential amino acid scores and 1. The second also presents the sum of squares of the residual for essential amino acid scores and 1 but with regard to only those amino acids, which scores are less than 1. The minima of these criteria at the set of variants for the content of ingredients are taken as targeted functions. The algorithm and the program of calculation were realized in the program environment Builder C++ 6.0. The macro flowchart of the algorithm is presented and detailed description of each block is given. The program interface before and after the start of the calculation module is shown. The main windows and interpretation of the presented data are described. An example of realization of the proposed mathematical apparatus when calculating a food model composition is given. Plant components (white kidney beans, flax, peanut, grit “Poltavskaya», dry red carrot) were used as an object of the research. Most plant proteins were incomplete. It is possible to regulate the chemical composition including correction of a protein profile by combination of plant raw materials. Analysis of alternative variants demonstrated that minimum essential amino acid score in the first composition was 0.79 (by the first criterion), in the second 1.0 (by the second criterion); the reference protein proportion in the mixture was 10.8 and 13.5, respectively, according to the first and second criterion. The comparative results by other quality indicators for protein in the mixture are also presented: the coefficient of amino acid score difference (CAASD), biological value (BV), coefficient of utility, essential amino acids index (IEAA).
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Chiang Hsieh, Lin-Han. "How Does the Effect Fade over Distance? An Inquiry into the Decay Pattern of Distance Effect on Property Values in the Case of Taipei, Taiwan." Land 10, no. 11 (2021): 1238. http://dx.doi.org/10.3390/land10111238.
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It is generally accepted that the perception of homeowners towards certain potential risks or amenities fades as distance from the risk or amenity increases. This study aims to illustrate the distance–decay pattern with an appropriate mathematical function. Distance–decay functions and parameters that yield the minimum residual sum of squares (RSS) for a given regression model are considered to be the optimal approximation for the pattern of decay. The effect of flood risk and mass rapid transit (MRT) accessibility on residential housing prices in Taipei, Taiwan, are used as examples to test the optimization process. The results indicate that the type of distance function affects both the significance and the magnitude of the regression coefficients. In the case of Taipei, concave functions provide better fits for both the flood risk and MRT accessibility. RSS reduction is up to 10% compared to the blank. Surprisingly, the impact range for the flood risk is found to be larger than that for MRT accessibility, which suggested that the impact range of perception for uncertain risks is larger than expected.