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Statistical inference for varying-coefficient partially linear errors-in-variables models with missing data
Authors:Hong-Xia Xu  Cheng-Xin Wu  Zhen-Long Chen
Institution:1. Department of Mathematics, Shanghai Maritime University, Shanghai, China;2. School of Mathematics and Statistics, Huangshan University, Huangshan, China;3. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China
Abstract: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:Empirical likelihood  errors-in-variables  inverse probability weighted  missing data  varying coefficient partially linear model
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