Empirical likelihood for linear regression models with missing responses

摘要

To make inference on beta (is an element of R-P) in a linear regression model Y-i = x'(beta)(i) + epsilon(i) with missing responses, Wang and Rao [Wang, Q. Rao, J.N.K., 2001. Empirical likelihood for linear regression models under imputation for missing responses. Canad. J. Statist. 29, 597-608.] constructed an empirical likelihood (EL) statistic based on the 'complete' data set after linear regression imputation which is asymptotically a sum of weighted chi(2)(1) variables with unknown weights. In this paper, we use a new method to produce a 'complete' data set for Y. Based on this data set, we construct an EL statistic on beta, and show that the EL statistic has the limiting distribution of chi(2)(p) which is used to construct confidence region on beta without adjustment. Results of a simulation study on the finite sample performance of EL-based confidence region on beta are reported.