应理学院数学系王勇教授和田波平教授的邀请，美国印第安娜大学南本德分校关忠教授将于7月18日在我校讲学并做学术报告，欢迎感兴趣的老师和同学参加交流。

报告题目：

Parameterizing  and Smoothing  using BernsteinPolynomials - An Efficient and Robust Method

地点：数学系会议室（格物楼503）

时间：2014年7月18日 下午15：00

报告摘要：Method of parameterizing and smoothing  the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed model. The approximating model turns out to be a mixture of  beta distributions beta(i+1, m-i+1), i = 0, ..., m, for some optimal degree m. A simple change-point estimating method for choosing optimal degree m of the Bernstein polynomials  is also presented.
    The proposed methods give maximum likelihood density estimate which is consistent in L2 distance at an almost parametric rate under some conditions. Simulation study shows that one can benefit from both the smoothness and the accuracy by using the proposed method. The proposed model can also be used to estimate some population parameters as mean. As illustration, the proposed methods are applied to three different type data sets including a microarray data set.

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