Some Applications Of Empirical Likelihood Inference

This dissertation focuses on some applications of the empirical likelihood (EL) method. The contents include the following aspects.In chapter1, we employ the EL method to construct confidence intervals for the population density function under an associated sample. It is proved that the EL ratio statistic is asymptotically chi-square distributed with one degree of freedom under some mild conditions. The simulation results show that the EL method performs better than the block EL method.In chapter2, we first use the EL method to construct confidence intervals for the nonparametric regression function with randomly truncated data. It is proved that the EL ratio statistic is asymptotically chi-square distributed with one degree of freedom under some mild conditions. The simulation results show that the EL method performs better than the normal-approximation-based method. Second, we employ the smoothed EL method to construct confidence intervals for the condi-tional quantile with randomly truncated data. It is proved that the smoothed EL ratio statistic is asymptotically chi-square distributed with one degree of freedom under some mild conditions. The simulation results show that the smoothed EL method performs better than the non-smoothed EL method.In chapter3. we first employ the EL method to construct confidence intervals for the nonparametric regression function under functional stationary ergodic data. It is proved that the EL ratio statistic is asymptotically chi-square distributed with one degree of freedom under some mild conditions. Second, we use the EL method to construct confidence intervals for the conditional quantile under functional station-ary ergodic data. It is proved that the EL ratio statistic is asymptotically chi-square distributed with one degree of freedom under some mild conditions.In chapter4, we consider the nonparametric M-estimator of a regression func-tion for functional stationary ergodic data. Under some regularity conditions, we employ the martingale-approximation-based method to obtain the weak consistency of the M-estimator and its asymptotic normality. The simulation results show that the M-estimator performs better than the Nadaraya-Watson estimator when the error distribution is heavy-tailed.