Inference in High-Dimensional Linear Measurement Error Models

2020/01/28 by Mengyan Li, Runze Li, Li, Mengyan +3
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2001.10142

openalex publication_date 2020/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and the corresponding one-step estimator. We further establish asymptotic properties of the newly proposed test statistic and the one-step estimator. Under local alternatives, we show that the limiting distribution of our corrected decorrelated score test statistic is non-central normal. The finite-sample performance of the proposed inference procedure is examined through simulation studies. We further illustrate the proposed procedure via an empirical analysis of a real data example.

Citations

• A general theory of hypothesis tests and confidence regions for sparse high dimensional models
• Confidence Bands for Coefficients in High Dimensional Linear Models with\n Error-in-variables

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