Empirical likelihood based inference for additive partial linear measurement error models

Abstract

This paper considers statistical inference for additive partial linear models when the linear covariate is measured with error.To improve the accuracy of the normal approximation based confidence intervals, we develop an empirical likelihood based statistic, which is shown to be asymptotically chi-square distributed.We emphasize the finite-sample performance of the proposed method by conducting simulation experiments.The method is used to analyze the relationship between semen quality and phthalate exposure from an environment study.