| Local
asymptotic normality and asymptotical minimax
efficiency of the MLE under random censorship |
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| 作者单位： | WANG Qihua(Department of Probability and Statistics, Peking University, Beijing 100871, China);JING Bingyi(Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China)
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| 基金项目： | the National Natural Science Foundation of China，the grant for the authors of excellent Ph.D dissertation in China，Hong Kong RGC |
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| 摘 要： |
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Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship |
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| Authors: | WANG Qihua JING Bingyi |
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| Institution: | 1. Department of Probability and Statistics, Peking University, Beijing 100871, China
2. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China |
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| Abstract: | Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient. |
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| Keywords: | local asymptotic normality asymptotic minimax efficiency maximum likelihood estimator random censorship |
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