제목 [학술세미나] [학과세미나] 10월 16일(금) 학과세미나 안내
작성일 2020-10-08 09:32:08
내용 [학과세미나] 10월 16일(금) 학과세미나 안내

▪제목 : Global rates of convergence in scale mixtures of uniform density estimation
▪연사 : 김경희 (고려대 통계학과)
▪일시 : 2020년 10월 16일(금) AM 11:00 – 12:00
▪진행 : ZOOM 활용 비대면 세미나
          (접속 링크 : https://snu-ac-kr.zoom.us/j/86100744437)
초 록
In this talk, we consider estimating a monotone decreasing density f_0 represented by a scale mixture of uniform densities. Pavlides and Wellner (2012) conjectured that the rates of convergence of the MLE would be n^{-1/3} with a log factor whose power depends on d, but the proof has not been provided yet. We first derive a general bound on the Hellinger accuracy of the MLE over convex classes. Using this bound with an entropy calculation, we provide a different proof for the convergence of the MLE for d=1. Then we consider a possible multidimensional extension. We can prove, for d >=2, that the rate is as conjectured by Pavlides and Wellner under the assumption that the density is bounded from above and below and supported on a compact region. We are exploring strategies for weakening the assumptions.
파일 세미나 안내_201016_김경희.hwp [14KB]