主 题：An alternating selection-optimization approach for an additive multi-index model
主讲人：朱力行教授
主持人：林华珍教授
时 间：2014年4月17日下午4:30
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：
朱力行教授，香港浸会大学数学系系主任，2013年荣获中国国家自然科学二等奖，2012年度荣获全球 20 0 1 - 2 0 1 0年度 S C I / S S C I高引用率学者（全世界排名 数学: 53/159, 统计： 19/48）。国家杰出青年基金获得者，教育部长江特聘教授。主持基金项目35项，累计资助金额1千多万港币。出版专著《Nonparametric Monte Carlo Tests and Their Applications》， 《非参数蒙特卡罗检验及其应用》及《 Empirical Likelihood in Nonparametric and Semiparametric Models》。发表论文255篇，其中在国际统计学前五刊物发表论文29篇。
内容提要：
Sufficient dimension reduction techniques are to deal with curse of dimensionality when the underlying model is of a very general semiparametric multi-index structure and to estimate the central subspace spanned by the indices. However, the cost is that they can only identify the central subspace/central mean subspace and its dimension, rather than the indices themselves. In this paper, we investigate estimation for an additive multi-index model (AMM) that is of an additive structure with indices. The problem for AMM involves determining and estimating the nonparametric component functions and estimating the corresponding indices in the model. Different from the classical sufficient dimension reduction techniques in the estimation of the subspace and dimensionality determination, we propose a new penalized method to implement the estimation of component functions and of indices simultaneously. To this end, we suggest an alternating determination-optimization algorithm to alternatively fit best model and estimate the indices.Estimation consistency is provided. Simulation studies are carried out to examine the performance of the new method and a real data example is also analysed for illustration.
