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Debiased and thresholded ridge regression for linear models with heteroskedastic and correlated errors.

Authors :
Zhang, Yunyi
Politis, Dimitris N
Source :
Journal of the Royal Statistical Society: Series B (Statistical Methodology); Apr2023, Vol. 85 Issue 2, p327-355, 29p
Publication Year :
2023

Abstract

High-dimensional linear models with independent errors have been well-studied. However, statistical inference on a high-dimensional linear model with heteroskedastic, dependent (and possibly nonstationary) errors is still a novel topic. Under such complex assumptions, the paper at hand introduces a debiased and thresholded ridge regression estimator that is consistent, and is able to recover the model sparsity. Moreover, we derive a Gaussian approximation theorem for the estimator, and apply a dependent wild bootstrap algorithm to construct simultaneous confidence interval and hypothesis tests for linear combinations of parameters. Numerical experiments with both real and simulated data show that the proposed estimator has good finite sample performance. Of independent interest is the development of a new class of heteroscedastic, (weakly) dependent, and nonstationary random variables that can be used as a general model for regression errors. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
13697412
Volume :
85
Issue :
2
Database :
Complementary Index
Journal :
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Publication Type :
Academic Journal
Accession number :
164283911
Full Text :
https://doi.org/10.1093/jrsssb/qkad006