2024/09/24 by Shijie Cui, Cui, Shijie, Xu Guo +5
Decision Sciences · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Methodology (stat.ME) #Scientific Measurement and Uncertainty Evaluation #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2409.16463
openalex publication_date 2024/09/24 · openalex created_date 2024/10/27 · openalex updated_date 2026/07/28
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.