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

• 成果类型: Article
• 署名作者: Zhang, Yunyi; Politis, Dimitris N.
• 署名单位: The Chinese University of Hong Kong, Shenzhen; University of California System; University of California San Diego; University of California System; University of California San Diego; University of California System; University of California San Diego
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad006
• 发表日期: 2023
• 页码: 327-355
• 关键词: wild bootstrap; variable selection; COVARIANCE-MATRIX; time-series; asymptotic properties; inference; Lasso; autocorrelation; Consistency; EIGENVALUE

摘要

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.