Weighted empirical likelihood inference

Abstract

A weighted empirical likelihood approach is proposed to take account of the heteroscedastic structure of the data. The resulting weighted empirical likelihood ratio statistic is shown to have a limiting chisquare distribution. A limited simulation study shows that the associated confidence intervals for a population mean or a regression coefficient have more accurate coverage probabilities and more balanced two-sided tail errors when the sample size is small or moderate. The proposed weighted empirical likelihood method also provides more efficient point estimators for a population mean in the presence of side information. Large sample resemblances between the weighted and the unweighted empirical likelihood estimators are characterized through high-order asymptotics and small sample discrepancies of these estimators are investigated through simulation. The proposed weighted approach reduces to the usual unweighted empirical likelihood method under a homogeneous variance structure.