Double-Estimation-Friendly Inference for High-Dimensional Measurement Error Models with Non-Sparse Adaptability

TL;DR

This paper presents a robust testing procedure for high-dimensional linear regression with measurement errors, effective under model misspecification and applicable to both sparse and non-sparse settings.

Contribution

It introduces a double robust score function and a corresponding test that work even when either the X-model or Y-model is misspecified, extending to high-dimensional non-sparse cases.

Findings

Asymptotic normality established in low-dimensional setting.

Method remains effective under model misspecification.

Demonstrated good performance in simulations and real data.

Abstract

In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is misspecified. We develop a double robust score function that maintains a zero expectation if one of the models is incorrect, and we construct a corresponding score test. We first show the asymptotic normality of our approach in a low-dimensional setting, and then extend it to the high-dimensional models. Our analysis of high-dimensional settings explores scenarios both with and without the sparsity condition, establishing asymptotic normality and non-trivial power performance under local alternatives. Simulation studies and real data analysis demonstrate the effectiveness of the proposed method.