讲座题目：Cram\'{e}r type  moderate deviations for the $L_1$  error of the Grenander estimator

主讲人：蒋辉 南京航空航天大学  

讲座时间：4月26日 15:00-16:00

讲座地点：综合大楼601会议室

主讲人简介：蒋辉,博士,南京航空航天大学理学院副教授,硕士生导师。现主要从事大偏差理论、过程研究。 

摘要：We consider the asymptotic behavior of the $L_1$  error between  a decreasing density $f$ and its nonparametric maximum likelihood  estimator $\hat{f}_n$. Using strong approximate, small ball estimates and  Cram\'{e}r type moderate deviations for  $\beta$-mixing random variables, some  (self-normalized) Cram\'{e}r type moderate deviations associated with  $\hat{f}_n$ are established. Then, we use these results to construct  asymptotical confidence intervals and asymptotical rejection regions of  hypothesis testing for the decreasing density functions. Moreover, we also  extend our results to the isotonic estimator of a monotone regression  function.