Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random

Liugen Xue

Scandinavian Journal of Statistics, 2009, vol. 36, issue 4, 671-685

Abstract: Abstract. A kernel regression imputation method for missing response data is developed. A class of bias‐corrected empirical log‐likelihood ratios for the response mean is defined. It is shown that any member of our class of ratios is asymptotically chi‐squared, and the corresponding empirical likelihood confidence interval for the response mean is constructed. Our ratios share some of the desired features of the existing methods: they are self‐scale invariant and no plug‐in estimators for the adjustment factor and asymptotic variance are needed; when estimating the non‐parametric function in the model, undersmoothing to ensure root‐n consistency of the estimator for the parameter is avoided. Since the range of bandwidths contains the optimal bandwidth for estimating the regression function, the existing data‐driven algorithm is valid for selecting an optimal bandwidth. We also study the normal approximation‐based method. A simulation study is undertaken to compare the empirical likelihood with the normal approximation method in terms of coverage accuracies and average lengths of confidence intervals.

Date: 2009
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