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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
A bias-corrected technique for constructing empirical likelihood ratio is used to study a semiparametric regression model with missing response data. We are interested in inference for the regression coefficients, the baseline function and the response mean. A class of empirical likelihood ratio functions for the parameters of interest are defined so that the undersmoothing for
estimating the baseline function is avoided, and the existing data-driven algorithm is also valid for selecting an optimal bandwidth. Our approach is to directly calibrate the empirical log-likelihood ratio so that the resulting ratio is asymptotically chi-squared. Also, a class of estimators for the parameters of interest are constructed, their asymptotic distributions are obtained, and the consistent estimators of asymptotic bias and variance are provided. Our results can be used to construct the confidence intervals for the parameters of interest. A simulation study is undertaken to compare the empirical likelihood with the normal approximation-based method in terms of coverage accuracies and average lengths of confidence intervals.
Keywords:Confidence interval;Empirical likelihood;Missing response data; Regression coefficient;Semiparametric regression model