Variable selection in quantile regression when the models have autoregressive errors

This paper considers a problem of variable selection in quantile regression with autoregressive errors. Recently, Wu and Liu (2009) investigated the oracle properties of the SCAD and adaptive-LASSO penalized quantile regressions under non identical but independent error assumption. We further relax...

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Bibliographic Details
Published in:Journal of the Korean Statistical Society Vol. 43; no. 4; pp. 513 - 530
Main Authors: Lim, Yaeji, Oh, Hee-Seok
Format: Journal Article
Language:English
Published: Singapore Elsevier B.V 01.12.2014
Springer Singapore
한국통계학회
Subjects:
Applied Statistics
Autoregressive error
Bayesian Inference
ES-algorithm
Penalized quantile regression
Pseudo data
SCAD penalty
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Variable selection
통계학
secondary
ES-algorithm
Pseudo data
SCAD penalty
Penalized quantile regression
Autoregressive error
primary
Variable selection
secondary 62J07
primary 62J05
ISSN:1226-3192, 2005-2863
Online Access:Get full text
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Summary:This paper considers a problem of variable selection in quantile regression with autoregressive errors. Recently, Wu and Liu (2009) investigated the oracle properties of the SCAD and adaptive-LASSO penalized quantile regressions under non identical but independent error assumption. We further relax the error assumptions so that the regression model can hold autoregressive errors, and then investigate theoretical properties for our proposed penalized quantile estimators under the relaxed assumption. Optimizing the objective function is often challenging because both quantile loss and penalty functions may be non-differentiable and/or non-concave. We adopt the concept of pseudo data by Oh et al. (2007) to implement a practical algorithm for the quantile estimate. In addition, we discuss the convergence property of the proposed algorithm. The performance of the proposed method is compared with those of the majorization-minimization algorithm (Hunter and Li, 2005) and the difference convex algorithm (Wu and Liu, 2009) through numerical and real examples.
Bibliography:G704-000337.2014.43.4.001
ISSN:1226-3192
2005-2863
DOI:10.1016/j.jkss.2014.07.002