  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.
