Empirical likelihood inference in linear regression with nonignorable missing response

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 most of them asymptotically converge to weighted chi-squared distributions when the tilting parameter is either given or estimated, except one of them is a chi-squared distribution. 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 analysed for illustration.