Inference under kernel regression imputation for missing response data is considered. An adjusted empirical likelihood approach to inference for the mean of the response variable is developed. A nonparametric version of Wilks' theorem is proved for the adjusted empirical log-likelihood ratio by showing that it has an asymptotic standard chi-squared distribution, and the corresponding empirical likelihood confidence interval for the mean is constructed. With auxiliary information, an empirical likelihood-based estimator is defined and an adjusted empirical log-likelihood ratio is derived. Asymptotic normality of the estimator is proved. Also, it is shown that the adjusted empirical log-likelihood ratio obeys Wilks' theorem. A simulation study is conducted to compare the adjusted empirical likelihood and the normal approximation methods in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparison is also made by simulation between the empirical likelihood-based estimator and related estimators. Our simulation indicates that the adjusted empirical likelihood method performs competitively and that the use of auxiliary information provides improved inferences.
"Empirical likelihood-based inference under imputation for missing response data." Ann. Statist. 30 (3) 896 - 924, June 2002. https://doi.org/10.1214/aos/1028674845