Statistical inference for varying-coefficient partially linear errors-in-variables models with missing data

Abstract

The purpose of this paper is twofold. First, we investigate estimations in varying-coefficient partially linear errors-in-variables models with covariates missing at random. However, the estimators are often biased due to the existence of measurement errors, the bias-corrected profile least-squares estimator and local liner estimators for unknown parametric and coefficient functions are obtained based on inverse probability weighted method. The asymptotic properties of the proposed estimators both for the parameter and nonparametric parts are established. Second, we study asymptotic distributions of an empirical log-likelihood ratio statistic and maximum empirical likelihood estimator for the unknown parameter. Based on this, more accurate confidence regions of the unknown parameter can be constructed. The methods are examined through simulation studies and illustrated by a real data analysis.

KEYWORDS and phrases:

• Empirical likelihood
• errors-in-variables
• inverse probability weighted
• missing data
• varying coefficient partially linear model

Acknowledgements

The authors thank the Editor, an Associated Editor and three referees for their constructive comments, which have led to a dramatic improvement of the earlier version of this article. This work is supported by National Natural Science Foundation of China (11401006), China Postdoctoral Science Foundation (2017M611083, 2018T110174), the Humanities and Social Sciences Research Project of Ministry of Education (18YJA910001), the National Statistical Science Research Project of China (2017LY51) and Zhejiang Provincial Key Research Project of Statistics (18TJZZ08).