Improved statistical inference on semiparametric varying-coefficient partially linear measurement error model

In this paper, we consider the estimation and goodness-of-fit test of a semiparametric varying-coefficient partially linear (SVCPL) model when both responses and part of covariates are measured with error. It is assumed that the true variables are measurable functions of some auxiliary variables. The often-used assumptions on the measurement error, such as a known error variance, a known distribution of the error variable, a validation sample or a repeated data set, are not required. The asymptotic properties of the proposed estimators and testing statistic are investigated. We show that the application of the measurement error structures can improve the efficiency of estimating and testing methods. The performances of the estimating and testing methods are illustrated by simulation studies and an application to a real data set.