Debiased and threshold ridge regression for linear model with heteroskedastic and dependent error

TL;DR

This paper develops a debiased and threshold ridge regression method for high-dimensional linear models with complex error structures, providing consistent estimation, Gaussian approximation, and a bootstrap-based inference procedure, with promising finite sample results.

Contribution

It introduces a novel debiased and threshold ridge regression approach tailored for models with dependent, non-stationary, and heteroskedastic errors, along with a bootstrap inference method.

Findings

Estimator shows favorable finite sample performance.

Gaussian approximation theorem established for the estimator.

Bootstrap method effectively constructs confidence intervals and tests.

Abstract

Focusing on a high dimensional linear model $y = X\beta + \epsilon$ with dependent, non-stationary, and heteroskedastic errors, this paper applies the debiased and threshold ridge regression method that gives a consistent estimator for linear combinations of $\beta$; and derives a Gaussian approximation theorem for the estimator. Besides, it proposes a dependent wild bootstrap algorithm to construct the estimator's confidence intervals and perform hypothesis testing. Numerical experiments on the proposed estimator and the bootstrap algorithm show that they have favorable finite sample performance. Research on a high dimensional linear model with dependent(non-stationary) errors is sparse, and our work should bring some new insights to this field.