Inference in high dimensional linear measurement error models

For a high dimensional linear model with a finite number of covariates measured with errors, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and a corresponding score type estimator. This work was motivated by a real data example, where both low dimensional phenotypic variables and high dimensional genotypic variables, single nucleotide polymorphisms (SNPs), are available. One of the phenotypic variables is of clinical interest but measured with error. As is standard in the literature, the high dimensional SNPs are assumed to be measured accurately. We show that the limiting distribution of our corrected decorrelated score test statistic is standard normal under the null hypothesis and retains power under the local alternatives around zero. We also establish the asymptotic normality of the newly proposed estimator, and hence asymptotic confidence intervals can be constructed. 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 the real data example mentioned above.