Double-Estimation-Friendly Inference for High-Dimensional Measurement Error Models with Non-Sparse Adaptability
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.
Cite
@article{arxiv.2409.16463,
title = {Double-Estimation-Friendly Inference for High-Dimensional Measurement Error Models with Non-Sparse Adaptability},
author = {Shijie Cui and Xu Guo and Songshan Yang and Zhe Zhang},
journal= {arXiv preprint arXiv:2409.16463},
year = {2025}
}