Estimation in a partially linear single-index model with missing response variables and error-prone covariates

Xin Qi,De-Hui Wang

doi:10.1186/s13660-015-0941-8

Abstract

In this paper, the authors study the partially linear single-index model when the covariate X is measured with additive error and the response variable Y is sometimes missing. Based on the least-squared technique, an imputation method is proposed to estimate the regression coefficients, single-index coefficients, and the nonparametric function, respectively. Thereafter, asymptotical normalities of the corresponding estimators are proved. A simulation experiment and an application to a diabetes study are used to illustrate our proposed method.

Highlights

1 Introduction We study the partially linear single-index model
Missing-data problems are always caused by design or accident, so the statisticians, such as Liu et al [ ] and Lai et al [ ], have paid a great attention to them
This paper, with the enlightenment of Lai et al [ ], focuses on estimating β, α, and the nonparametric function g(·) with imputation method when the covariate X is measured with additive error and the response variable Y is sometimes missing in the model ( . )

Summary

Introduction

Observations are often measured with errors, as can be seen in the papers of Liang et al [ ] and Chen et al [ ] Those studies of the observations characterized by inaccurate measures are based on the complete data set. Qi and Wang Journal of Inequalities and Applications (2016) 2016:11 missing response Taking both measurement errors in the covariates and the missing response variables into account, Liang et al [ ], Wei et al [ ] and Wei [ ] have done some work in the partially linear model, in the partially linear additive model and in the partially linear varying-coefficient model, respectively. This paper, with the enlightenment of Lai et al [ ], focuses on estimating β, α, and the nonparametric function g(·) with imputation method when the covariate X is measured with additive error and the response variable Y is sometimes missing in the model

Methodology

Imputation method

Asymptotic results

Findings

Methods