主 题：Maximum Smoothed Likelihood Component Density Estimation in Mixture Models with Known Mixing Proportions
主讲人：Tao Yu 博士
主持人：林华珍教授
时 间： 2014年7月16日（星期三）下午2:00-3:00
地 点：通博楼B座212学术会议室
主办单位：统计学院 统计研究中心 科研处
主讲人简介：
Dr. Yu, Tao received his B.S. degree and M.S. in Mathematics and Probability & Statistics from Nankai University, China, in 2001 and 2004 respectively. He obtained his Ph.D. degree from University of Wisconsin-Madison, USA, in 2009. After that, he is appointedassistant professor by Department of Statistics and Applied Probability, National University of Singapore. Tao Yu’s research interest include Neuroinformatics, Bioinformatics and Biostatistics, Statistical Inference for High-Dimensional Model, Non- and Semi-parametric Estimation & Inference.
内容提要：
In this paper, we propose a maximum smoothed likelihood method to estimate the component density functions of mixture models, in which the mixing proportions are known and may di_er among observations. The proposed estimates maximize a smoothed log likelihood function and inherit all the important properties of probability density functions. A majorization-minimization algorithm is suggested to compute the proposed estimates numerically. In theory, we show that starting from any initial value, this algorithm increases the smoothed likelihood function and further leads to estimates that maximize the smoothed likelihood function. This indicates the convergence of the algorithm. Furthermore, we theoretically establish the L1 consistency of our proposed estimators. An adaptive procedure is suggested to choose the bandwidths in our estimation procedure. Simulation studies show that the proposed method is more e_cient than the existing method in terms of integrated square errors. A real data example is further analyzed.
