Inference in High-Dimensional Linear Measurement Error Models

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.

References in corpus (5)

• Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
• High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity
• Sparse recovery under matrix uncertainty
• Measurement Error in Lasso: Impact and Correction
• Confidence Bands for Coefficients in High Dimensional Linear Models with Error-in-variables

Cited by in corpus (1)

• Scalable Interpretable Learning for Multi-Response Error-in-Variables Regression