题目：Bernstein Polynomial Model for Density Estimation

报告人： Prof. Zhong Guan  （ Indiana   University  South  Bend ）

摘要：A method of parameterizing and smoothing the unknown underlying distributions using Bernstein type polynomials with positive coefficients is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed model which turns out to be a mixture of the beta distributions, beta(i+1, m-i+1),  i="0," ..., m, for some optimal degree m. A simple change-point estimating method for choosing the optimal degree m of the approximate model Bernstein polynomials is presented. Using the acceptance-rejection argument for generating pseudorandom numbers we showed that the proposed method  gives a maximum likelihood density estimate which is consistent in L2 distance at a nearly parametric rate O((log n)^2/n)  under some conditions. Simulation study shows that one can benefit from both the smoothness and the efficiency by using the proposed method. The proposed methods are applied to some real data sets.

时间：7月11日（周六）上午9:30-10:30

地点：澳门沙金在线平台北一区文科楼 708 教室

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