Score function-based tests for ultrahigh-dimensional linear models

TL;DR

This paper develops and extends score function-based tests for assessing the significance of specific coefficients in ultrahigh-dimensional linear models, addressing issues of high correlation and improving test power.

Contribution

It introduces an orthogonalized score function-based test with debiasing and variance reduction, applicable under weaker conditions in ultrahigh-dimensional settings.

Findings

Extended the limiting distributions under weaker conditions.

Proposed an orthogonalized test with debiasing and variance reduction.

Demonstrated improved finite-sample performance through simulations.

Abstract

In this paper, we investigate score function-based tests to check the significance of an ultrahigh-dimensional sub-vector of the model coefficients when the nuisance parameter vector is also ultrahigh-dimensional in linear models. We first reanalyze and extend a recently proposed score function-based test to derive, under weaker conditions, its limiting distributions under the null and local alternative hypotheses. As it may fail to work when the correlation between testing covariates and nuisance covariates is high, we propose an orthogonalized score function-based test with two merits: debiasing to make the non-degenerate error term degenerate and reducing the asymptotic variance to enhance power performance. Simulations evaluate the finite-sample performances of the proposed tests, and a real data analysis illustrates its application.