Empirical Likelihood Inference for the Mean Difference of Two Nonparametric Populations with Missing Data

摘要

Let Z = (X, Y)~T be a bivariate population with mean EZ = (EX,EY)~T and mean difference θ = EY-EX. Based on the 'complete' data after inverse probability weighted (IPW) imputation, we make empirical likelihood (EL) inference for θ. It is shown that the limiting distribution of the EL statistic under IPW imputation is x_1~2 unlike the EL statistic based on the original nonparametric regression imputation approach which is asymptotically distributed as a scaled chi-squared distribution. This research has enhanced the EL method based on the original nonparametric regression imputation at two aspects: (1) it releases the burden of estimating adjustment coefficients; (2) it can improve the accuracy of the EL confidence intervals.