TY - JOUR

T1 - Empirical likelihood inference in linear regression with nonignorable missing response

AU - Niu, Cuizhen

AU - Guo, Xu

AU - Xu, Wangli

AU - ZHU, Lixing

N1 - Funding Information:
The research was supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (No. 14XNH102), National Natural Science Foundation of China (No. 11071253 ) and a grant from the Research Grants Council of Hong Kong (No. HKBU2040/13P ). The authors thank the editor, the associate editor and two anonymous referees for their constructive comments and suggestions which led to a substantial improvement of an early manuscript.

PY - 2014/11

Y1 - 2014/11

N2 - Parameter estimation for nonignorable nonresponse data is a challenging issue as the missing mechanism is unverified in practice and the parameters of response probabilities need to be estimated. This article aims at applying the empirical likelihood to construct the confidence intervals for the parameters of interest in linear regression models with nonignorable missing response data and the nonignorable missing mechanism is specified as an exponential tilting model. Three empirical likelihood ratio functions based on weighted empirical likelihood and imputed empirical likelihood are defined. It is proved that, except one that is chi-squared distributed, all the others are asymptotically weighted chi-squared distributed whenever the tilting parameter is either given or estimated. The asymptotic normality for the related parameter estimates is also investigated. Simulation studies are conducted to evaluate the finite sample performance of the proposed estimates in terms of coverage probabilities and average widths for the confidence intervals of parameters. A real data analysis is analyzed for illustration.

AB - Parameter estimation for nonignorable nonresponse data is a challenging issue as the missing mechanism is unverified in practice and the parameters of response probabilities need to be estimated. This article aims at applying the empirical likelihood to construct the confidence intervals for the parameters of interest in linear regression models with nonignorable missing response data and the nonignorable missing mechanism is specified as an exponential tilting model. Three empirical likelihood ratio functions based on weighted empirical likelihood and imputed empirical likelihood are defined. It is proved that, except one that is chi-squared distributed, all the others are asymptotically weighted chi-squared distributed whenever the tilting parameter is either given or estimated. The asymptotic normality for the related parameter estimates is also investigated. Simulation studies are conducted to evaluate the finite sample performance of the proposed estimates in terms of coverage probabilities and average widths for the confidence intervals of parameters. A real data analysis is analyzed for illustration.

KW - Empirical likelihood inference

KW - Imputed empirical likelihood

KW - Inverse probability weighted

KW - Linear regression

KW - Nonignorable missing response

UR - http://www.scopus.com/inward/record.url?scp=84902189135&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2014.05.005

DO - 10.1016/j.csda.2014.05.005

M3 - Article

AN - SCOPUS:84902189135

VL - 79

SP - 91

EP - 112

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

ER -