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Journal articles on the topic 'Heteroscedastic Multivariate Linear Regression'

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Author: Grafiati

Published: 10 March 2023

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1

Zhang, X., C. E. Lee, and X. Shao. "Envelopes in multivariate regression models with nonlinearity and heteroscedasticity." Biometrika 107, no. 4 (June 17, 2020): 965–81. http://dx.doi.org/10.1093/biomet/asaa036.

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Summary Envelopes have been proposed in recent years as a nascent methodology for sufficient dimension reduction and efficient parameter estimation in multivariate linear models. We extend the classical definition of envelopes in Cook et al. (2010) to incorporate a nonlinear conditional mean function and a heteroscedastic error. Given any two random vectors ${X}\in\mathbb{R}^{p}$ and ${Y}\in\mathbb{R}^{r}$, we propose two new model-free envelopes, called the martingale difference divergence envelope and the central mean envelope, and study their relationships to the standard envelope in the context of response reduction in multivariate linear models. The martingale difference divergence envelope effectively captures the nonlinearity in the conditional mean without imposing any parametric structure or requiring any tuning in estimation. Heteroscedasticity, or nonconstant conditional covariance of ${Y}\mid{X}$, is further detected by the central mean envelope based on a slicing scheme for the data. We reveal the nested structure of different envelopes: (i) the central mean envelope contains the martingale difference divergence envelope, with equality when ${Y}\mid{X}$ has a constant conditional covariance; and (ii) the martingale difference divergence envelope contains the standard envelope, with equality when ${Y}\mid{X}$ has a linear conditional mean. We develop an estimation procedure that first obtains the martingale difference divergence envelope and then estimates the additional envelope components in the central mean envelope. We establish consistency in envelope estimation of the martingale difference divergence envelope and central mean envelope without stringent model assumptions. Simulations and real-data analysis demonstrate the advantages of the martingale difference divergence envelope and the central mean envelope over the standard envelope in dimension reduction.

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2

Shao, Jun, and J. N. K. Rao. "Jackknife inference for heteroscedastic linear regression models." Canadian Journal of Statistics 21, no. 4 (December 1993): 377–95. http://dx.doi.org/10.2307/3315702.

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3

Leslie, David S., Robert Kohn, and David J. Nott. "A general approach to heteroscedastic linear regression." Statistics and Computing 17, no. 2 (January 30, 2007): 131–46. http://dx.doi.org/10.1007/s11222-006-9013-8.

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4

Su, Li Yun, and Chun Hua Wang. "Two-Stage Local Polynomial Regression Method for Image Heteroscedastic Noise Removal." Advanced Materials Research 860-863 (December 2013): 2936–39. http://dx.doi.org/10.4028/www.scientific.net/amr.860-863.2936.

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In this paper, we introduce the extension of local polynomial fitting to the linear heteroscedastic regression model and its applications in digital image heteroscedastic noise removal. For better image noise removal with heteroscedastic energy, firstly, the local polynomial regression is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. Due to non-parametric technique of local polynomial estimation, we do not need to know the heteroscedastic noise function. Therefore, we improve the estimation precision, when the heteroscedastic noise function is unknown. Numerical simulations results show that the proposed method can improve the image quality of heteroscedastic noise energy.

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5

Ounpraseuth, Songthip T., Phil D. Young, Johanna S. van Zyl, Tyler W. Nelson, and Dean M. Young. "Linear Dimension Reduction for Multiple Heteroscedastic Multivariate Normal Populations." Open Journal of Statistics 05, no. 04 (2015): 311–33. http://dx.doi.org/10.4236/ojs.2015.54033.

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6

Monteiro, Alessandra da Rocha Duailibe, Thiago de Sá Feital, and José Carlos Pinto. "A Numerical Procedure for Multivariate Calibration Using Heteroscedastic Principal Components Regression." Processes 9, no. 9 (September 21, 2021): 1686. http://dx.doi.org/10.3390/pr9091686.

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Many methods have been developed to allow for consideration of measurement errors during multivariate data analyses. The incorporation of the error structure into the analytical framework, usually described in terms of the covariance matrix of measurement errors, can provide better model estimation and prediction. However, little effort has been made to evaluate the effects of heteroscedastic measurement uncertainties on multivariate analyses when the covariance matrix of measurement errors changes with the measurement conditions. For this reason, the present work describes a new numerical procedure for analyses of heteroscedastic systems (heteroscedastic principal component regression or H-PCR) that takes into consideration the variations of the covariance matrix of measurement fluctuations. In order to illustrate the proposed approach, near infrared (NIR) spectra of xylene and toluene mixtures were measured at different temperatures and stirring velocities and the obtained data were used to build calibration models with different multivariate techniques, including H-PCR. Modeling of available xylene–toluene NIR data revealed that H-PCR can be used successfully for calibration purposes and that the principal directions obtained with the proposed approach can be quite different from the ones calculated through standard PCR, when heteroscedasticity is disregarded explicitly.

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7

Thinh, Raksmey, Klairung Samart, and Naratip Jansakul. "Linear regression models for heteroscedastic and non-normal data." ScienceAsia 46, no. 3 (2020): 353. http://dx.doi.org/10.2306/scienceasia1513-1874.2020.047.

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8

Gijbels, I., and I. Vrinssen. "Robust estimation and variable selection in heteroscedastic linear regression." Statistics 53, no. 3 (February 18, 2019): 489–532. http://dx.doi.org/10.1080/02331888.2019.1579215.

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9

Linke, Yu Yu. "Two-Step Estimation in a Heteroscedastic Linear Regression Model." Journal of Mathematical Sciences 231, no. 2 (April 27, 2018): 206–17. http://dx.doi.org/10.1007/s10958-018-3816-y.

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10

Faraway, Julian J., and Jiayang Sun. "Simultaneous Confidence Bands for Linear Regression with Heteroscedastic Errors." Journal of the American Statistical Association 90, no. 431 (September 1995): 1094–98. http://dx.doi.org/10.1080/01621459.1995.10476612.

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11

Kuk, Anthony Y. C. "Nonparametrically Weighted Least Squares Estimation in Heteroscedastic Linear Regression." Biometrical Journal 41, no. 4 (July 1999): 401–10. http://dx.doi.org/10.1002/(sici)1521-4036(199907)41:4<401::aid-bimj401>3.0.co;2-5.

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12

Su, Liyun, Yanyong Zhao, and Tianshun Yan. "Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics." Discrete Dynamics in Nature and Society 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/696927.

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We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations.

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13

Kirlitsa, Valery P. "Construction D-optimal designs of experiments for linear multiple regression with heteroscedastic observations." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (July 12, 2019): 27–33. http://dx.doi.org/10.33581/2520-6508-2019-2-27-33.

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In article the problem of construction exact D-optimal designs of experiments for linear multiple regression in a case when variance of errors of observations depend on a point in which is made is investigated. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct D-optimal continues designs of experiments. For linear multiple regression with three factors it is constructed five different types of D-optimal continues designs of experiments with heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.

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14

Dorfman, Alan. "A note on millers's empirical weights for heteroscedastic linear regression." Communications in Statistics - Theory and Methods 17, no. 10 (January 1988): 3521–35. http://dx.doi.org/10.1080/03610928808829818.

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15

Shen, Silian, and Changlin Mei. "Estimation of the Variance Function in Heteroscedastic Linear Regression Models." Communications in Statistics - Theory and Methods 38, no. 7 (March 24, 2009): 1098–112. http://dx.doi.org/10.1080/03610920802374061.

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16

Schick, Anton. "Efficient estimates in linear and nonlinear regression with heteroscedastic errors." Journal of Statistical Planning and Inference 58, no. 2 (March 1997): 371–87. http://dx.doi.org/10.1016/s0378-3758(96)00077-8.

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17

You, Jinhong, Gemai Chen, and Yong Zhou. "Statistical inference of partially linear regression models with heteroscedastic errors." Journal of Multivariate Analysis 98, no. 8 (September 2007): 1539–57. http://dx.doi.org/10.1016/j.jmva.2007.06.011.

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18

Molstad, Aaron J., and Adam J. Rothman. "Indirect multivariate response linear regression." Biometrika 103, no. 3 (August 24, 2016): 595–607. http://dx.doi.org/10.1093/biomet/asw034.

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19

Andronov, Alexander. "Markov-modulated multivariate linear regression." Acta et Commentationes Universitatis Tartuensis de Mathematica 21, no. 1 (July 3, 2017): 43. http://dx.doi.org/10.12697/acutm.2017.21.03.

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20

Kirlitsa, Valery P. "D-optimal experimental designs for linear multiple regression under heteroscedastic observations." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (July 30, 2020): 59–67. http://dx.doi.org/10.33581/2520-6508-2020-2-59-67.

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The problem of construction of «continuous» (number of observations is not fixed) and «exact» (number of observations is fixed) D-optimal experimental designs for linear multiple regression in the case when variance of errors of observations depends on regressor value is studied in this paper. Families of functions that determine heteroscedastic observations are found for which it is possible to construct «continuous» and «exact» D-optimal experimental designs. «Continuous» D-optimal experimental designs under four different types of heteroscedasticity are constructed for linear multiple regression with three regressors.

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21

Muhammad, Faqir, Muhammad Aslam, and G. R. Pasha. "Adaptive Estimation of Heteroscedastic Linear Regression Model Using Probability Weighted Moments." Journal of Modern Applied Statistical Methods 7, no. 2 (November 1, 2008): 501–5. http://dx.doi.org/10.22237/jmasm/1225512840.

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22

Inoue, Kiyoshi. "Iterative weighted least-squares estimates in a heteroscedastic linear regression model." Journal of Statistical Planning and Inference 110, no. 1-2 (January 2003): 133–46. http://dx.doi.org/10.1016/s0378-3758(01)00285-3.

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23

Alshaybawee, Taha, Rahim Alhamzawi, Habshah Midi, and Intisar Ibrahim Allyas. "Bayesian variable selection and coefficient estimation in heteroscedastic linear regression model." Journal of Applied Statistics 45, no. 14 (February 7, 2018): 2643–57. http://dx.doi.org/10.1080/02664763.2018.1432576.

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24

Dorugade, Ashok Vithoba. "Improved Ridge Estimator in Linear Regression with Multicollinearity, Heteroscedastic Errors and Outliers." Journal of Modern Applied Statistical Methods 15, no. 2 (November 1, 2016): 362–81. http://dx.doi.org/10.22237/jmasm/1478002860.

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25

Holmes, C. C., and B. K. Mallick. "Bayesian regression with multivariate linear splines." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63, no. 1 (February 2001): 3–17. http://dx.doi.org/10.1111/1467-9868.00272.

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26

Cook, R. Dennis, and Xin Zhang. "Simultaneous Envelopes for Multivariate Linear Regression." Technometrics 57, no. 1 (January 2, 2015): 11–25. http://dx.doi.org/10.1080/00401706.2013.872700.

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27

Eck, Daniel J. "Bootstrapping for multivariate linear regression models." Statistics & Probability Letters 134 (March 2018): 141–49. http://dx.doi.org/10.1016/j.spl.2017.11.001.

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28

Chiou, Jeng-Min, Ya-Fang Yang, and Yu-Ting Chen. "Multivariate functional linear regression and prediction." Journal of Multivariate Analysis 146 (April 2016): 301–12. http://dx.doi.org/10.1016/j.jmva.2015.10.003.

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29

Rodríguez del Águila, M. M., and N. Benítez-Parejo. "Simple linear and multivariate regression models." Allergologia et Immunopathologia 39, no. 3 (May 2011): 159–73. http://dx.doi.org/10.1016/j.aller.2011.02.001.

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30

Beyad, Yaser, and Marcel Maeder. "Multivariate linear regression with missing values." Analytica Chimica Acta 796 (September 2013): 38–41. http://dx.doi.org/10.1016/j.aca.2013.08.027.

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31

Lee, Yi-Tzu, and Thomas Mathew. "Tolerance regions in multivariate linear regression." Journal of Statistical Planning and Inference 126, no. 1 (November 2004): 253–71. http://dx.doi.org/10.1016/j.jspi.2003.07.002.

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32

Wörz, Sascha, and Heinz Bernhardt. "A note on multivariate linear regression." Communications in Statistics - Theory and Methods 47, no. 19 (March 13, 2018): 4785–90. http://dx.doi.org/10.1080/03610926.2018.1445863.

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33

Vicari, Donatella, and Maurizio Vichi. "Multivariate linear regression for heterogeneous data." Journal of Applied Statistics 40, no. 6 (June 2013): 1209–30. http://dx.doi.org/10.1080/02664763.2013.784896.

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34

Li, Xiongya, Xiuqin Bai, and Weixing Song. "Robust mixture multivariate linear regression by multivariate Laplace distribution." Statistics & Probability Letters 130 (November 2017): 32–39. http://dx.doi.org/10.1016/j.spl.2017.06.028.

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35

Feigelson, E. D., and G. J. Babu. "Statistical Methodology for Large Astronomical Surveys." Symposium - International Astronomical Union 179 (1998): 363–70. http://dx.doi.org/10.1017/s0074180900129043.

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Multiwavelength surveys present a variety of challenging statistical problems: raw data processing, source identification, source characterization and classification, and interrelations between multiwavelength properties. For these last two issues, we discuss the applicability of standard and new multivariate statistical techniques. Traditional methods such as ANOVA, principal components analysis, cluster analysis, and tests for multivariate linear hypotheses are underutilized in astronomy and can be very helpful. Newer statistical methods such as projection pursuit, multivariate splines, and visualization tools such as XGobi are briefly introduced. However, multivariate databases from astronomical surveys present significant challenges to the statistical community. These include treatments of heteroscedastic measurement errors, censoring and truncation due to flux limits, and parameter estimation for nonlinear astrophysical models.

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36

Hsiao, Chih-Wen, Ya-Chuan Chan, Mei-Yu Lee, and Hsi-Peng Lu. "Heteroscedasticity and Precise Estimation Model Approach for Complex Financial Time-Series Data: An Example of Taiwan Stock Index Futures before and during COVID-19." Mathematics 9, no. 21 (October 26, 2021): 2719. http://dx.doi.org/10.3390/math9212719.

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In this paper, we provide a mathematical and statistical methodology using heteroscedastic estimation to achieve the aim of building a more precise mathematical model for complex financial data. Considering a general regression model with explanatory variables (the expected value model form) and the error term (including heteroscedasticity), the optimal expected value and heteroscedastic model forms are investigated by linear, nonlinear, curvilinear, and composition function forms, using the minimum mean-squared error criterion to show the precision of the methodology. After combining the two optimal models, the fitted values of the financial data are more precise than the linear regression model in the literature and also show the fitted model forms in the example of Taiwan stock price index futures that has three cases: (1) before COVID-19, (2) during COVID-19, and (3) the entire observation time period. The fitted mathematical models can apparently show how COVID-19 affects the return rates of Taiwan stock price index futures. Furthermore, the fitted heteroscedastic models also show how COVID-19 influences the fluctuations of the return rates of Taiwan stock price index futures. This methodology will contribute to the probability of building algorithms for computing and predicting financial data based on mathematical model form outcomes and assist model comparisons after adding new data to a database.

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37

Guney, Yesim, Olcay Arslan, and Fulya Gokalp Yavuz. "Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm." Journal of Multivariate Analysis 191 (September 2022): 105026. http://dx.doi.org/10.1016/j.jmva.2022.105026.

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38

Fiorentini, Gabriele, Enrique Sentana, and Giorgio Calzolari. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models With StudenttInnovations." Journal of Business & Economic Statistics 21, no. 4 (October 2003): 532–46. http://dx.doi.org/10.1198/073500103288619232.

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39

Das, Debraj, and S. N. Lahiri. "Distributional consistency of the lasso by perturbation bootstrap." Biometrika 106, no. 4 (June 30, 2019): 957–64. http://dx.doi.org/10.1093/biomet/asz029.

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Summary The lasso is a popular estimation procedure in multiple linear regression. We develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model. We allow the underlying covariates to be either random or nonrandom, and show that the proposed bootstrap method works irrespective of the nature of the covariates. We also investigate finite-sample properties of the proposed bootstrap method in a moderately large simulation study.

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40

Liang, Han-Ying, and Bing-Yi Jing. "Strong Consistency of Estimators for Heteroscedastic Partly Linear Regression Model under Dependent Samples." Journal of Applied Mathematics and Stochastic Analysis 15, no. 3 (January 1, 2002): 207–19. http://dx.doi.org/10.1155/s1048953302000187.

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In this paper we are concerned with the heteroscedastic regression model yi=xiβ+g(ti)+σiei, 1≤i≤n under correlated errors ei, where it is assumed that σi2=f(ui), the design points (xi,ti,ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance ei are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator.

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41

Begum, Nelufa, and Maxwell L. King. "Most mean powerful test for testing heteroscedastic disturbances in the linear regression model." Model Assisted Statistics and Applications 1, no. 1 (December 15, 2005): 9–16. http://dx.doi.org/10.3233/mas-2006-1103.

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42

You, Jinhong, Xian Zhou, and Yong Zhou. "Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors." Journal of Multivariate Analysis 101, no. 5 (May 2010): 1079–101. http://dx.doi.org/10.1016/j.jmva.2010.01.003.

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43

Schick, Anton, and Yilin Zhu. "Maximum Empirical Likelihood Estimation In A Heteroscedastic Linear Regression ModelWith Possibly Missing Responses." Sri Lankan Journal of Applied Statistics 5, no. 4 (December 15, 2014): 209. http://dx.doi.org/10.4038/sljastats.v5i4.7791.

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44

Wilcox, Rand R. "Linear regression: robust heteroscedastic confidence bands that have some specified simultaneous probability coverage." Journal of Applied Statistics 44, no. 14 (November 24, 2016): 2564–74. http://dx.doi.org/10.1080/02664763.2016.1257591.

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45

EA, Emrah Altun, Morad Alizadeh, Thiago Ramires, and Edwin Ortega. "Generalized Odd Power Cauchy Family and Its Associated Heteroscedastic Regression Model." Statistics, Optimization & Information Computing 9, no. 3 (July 10, 2021): 516–28. http://dx.doi.org/10.19139/soic-2310-5070-765.

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This study introduces a generalization of the odd power Cauchy family by adding one more shape parameter togain more flexibility modeling the complex data structures. The linear representations for the density, moments, quantile,and generating functions are derived. The model parameters are estimated employing the maximum likelihood estimationmethod. The Monte Carlo simulations are performed under different parameter settings and sample sizes for the proposedmodels. In addition, we introduce a new heteroscedastic regression model based on the special member of the proposedfamily. Three data sets are analyzed with competitive and proposed models.

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46

Orlandi, Manuel, Margarita Escudero-Casao, and Giulia Licini. "Nucleophilicity Prediction via Multivariate Linear Regression Analysis." Journal of Organic Chemistry 86, no. 4 (February 3, 2021): 3555–64. http://dx.doi.org/10.1021/acs.joc.0c02952.

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47

Breiman, Leo, and Jerome H. Friedman. "Predicting Multivariate Responses in Multiple Linear Regression." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 59, no. 1 (February 1997): 3–54. http://dx.doi.org/10.1111/1467-9868.00054.

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48

Yang, L., and R. Tschernig. "Multivariate bandwidth selection for local linear regression." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61, no. 4 (November 1999): 793–815. http://dx.doi.org/10.1111/1467-9868.00203.

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49

Liu, Wei, Yang Han, Fang Wan, Frank Bretz, and Anthony J. Hayter. "Simultaneous Confidence Tubes in Multivariate Linear Regression." Scandinavian Journal of Statistics 43, no. 3 (March 17, 2016): 879–85. http://dx.doi.org/10.1111/sjos.12217.

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50

Mantz, Adam B. "A Gibbs sampler for multivariate linear regression." Monthly Notices of the Royal Astronomical Society 457, no. 2 (February 1, 2016): 1279–88. http://dx.doi.org/10.1093/mnras/stv3008.

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