Quantile regression for linear models with autoregressive errors using EM algorithm

In this paper, we consider the quantile linear regression models with autoregressive errors. By incorporating the expectation–maximization algorithm into the considered model, the iterative weighted least square estimators for quantile regression parameters and autoregressive parameters are derived. Finally, the proposed procedure is illustrated by simulations and a real data example.

[1]  M. Fuentes,et al.  Journal of the American Statistical Association Bayesian Spatial Quantile Regression Bayesian Spatial Quantile Regression , 2022 .

[2]  Qianqian Zhu,et al.  Linear Quantile Regression Based on EM Algorithm , 2014 .

[3]  D. Oakes Direct calculation of the information matrix via the EM , 1999 .

[4]  Yunlu Jiang,et al.  Penalized weighted composite quantile regression in the linear regression model with heavy-tailed autocorrelated errors , 2014 .

[5]  R. Ramanathan,et al.  Introductory Econometrics With Applications , 1989 .

[6]  Chiao-Yi Yang,et al.  Estimation of Linear Regression Models with Serially Correlated Errors , 2021 .

[7]  P. Embrechts,et al.  Quantitative Risk Management: Concepts, Techniques, and Tools , 2005 .

[8]  Taewook Lee,et al.  Penalized regression models with autoregressive error terms , 2013 .

[9]  Dedi Rosadi,et al.  Second-order least-squares estimation for regression models with autocorrelated errors , 2014, Comput. Stat..

[10]  Rongning Wu,et al.  Shrinkage estimation for linear regression with ARMA errors , 2012 .

[11]  R. Koenker Quantile Regression: Name Index , 2005 .

[12]  Yuzhu Tian,et al.  Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates , 2016, Comput. Stat..

[13]  Yang Li,et al.  Quantile Correlations and Quantile Autoregressive Modeling , 2012, 1209.6487.

[14]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[15]  R. Tibshirani,et al.  An introduction to the bootstrap , 1993 .

[16]  Keming Yu,et al.  Bayesian quantile regression , 2001 .

[17]  Robert Lund,et al.  Revisiting simple linear regression with autocorrelated errors , 2004 .

[18]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[19]  Hee-Seok Oh,et al.  Variable selection in quantile regression when the models have autoregressive errors , 2014 .

[20]  M. Bottai,et al.  Mixed-Effects Models for Conditional Quantiles with Longitudinal Data , 2009, The international journal of biostatistics.

[21]  F. Graybill An introduction to linear statistical models , 1961 .

[22]  Peter Filzmoser,et al.  Robust second-order least-squares estimation for regression models with autoregressive errors , 2019 .

[23]  J. McKean,et al.  A double bootstrap method to analyze linear models with autoregressive error terms. , 2000, Psychological methods.

[24]  S. Ejaz Ahmed,et al.  Shrinkage estimation and variable selection in multiple regression models with random coefficient autoregressive errors , 2014 .

[25]  Dries F. Benoit,et al.  Bayesian adaptive Lasso quantile regression , 2012 .

[26]  M. Bottai,et al.  Quantile regression for longitudinal data using the asymmetric Laplace distribution. , 2007, Biostatistics.

[27]  Anton Schick,et al.  Regression Models with Time Series Errors , 1999 .

[28]  Shalabh,et al.  Linear Models and Generalizations: Least Squares and Alternatives , 2007 .

[29]  H. Kozumi,et al.  Gibbs sampling methods for Bayesian quantile regression , 2011 .

[30]  Heng Lian,et al.  Bayesian Tobit quantile regression with single-index models , 2015 .

[31]  Genya Kobayashi,et al.  Bayesian analysis of quantile regression for censored dynamic panel data , 2012, Comput. Stat..

[32]  D. Cochrane,et al.  Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms , 1949 .