In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standar...In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chiqsquare distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.11171188, 11201499 and 10921101)Natural Science Foundation of Shandong Province (Grant Nos. ZR2010AZ001 and ZR2011AQ007)+1 种基金Shandong Provincial Scientific Research Reward Foundation for Excellent Young and MiddleAged Scientists (Grant No. BS2011SF006)K.C. Wong-HKBU Fellowship Program for Mainland Visiting Scholars 2010-11
文摘In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chiqsquare distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.
