光华讲坛——社会名流与企业家论坛第5286期

主 题：Nonparametric Homogeneity Pursuit in Functional-Coefficient Models

主讲人：英国约克大学 张文扬教授

主持人：林华珍教授

时 间：2018年4月16日（星期二）下午4:00-5:00

地 点：弘远楼408会议室

主办单位：统计研究中心 统计学院 科研处

主讲人简介：

张文扬教授是英国约克大学统计学首席教授,统计学顶级期刊JASA的Associate Editor,IMS(国际数理统计学会)教材-专著系列的编委会委员，英国皇家统计学会科研分会委员（历史上仅有三位华人担任该委员会委员）。他在非参数统计、时间序列、统计计算、生存分析、结构方程模型等领域发表了很多高质量的研究论文，其中有12篇文章发表在统计学顶级期刊AOS,JASA,JRSSB及Biometrika上。他和合作者1999年合作发表在AOS的文章，已经成为半参数变系数模型（VCM）研究中的经典工作，几乎被每一篇有关VCM文章所引用，文章的引用次数超过600次（Google citations）。他2002年发表在Genetics 上另一篇论文研究Bayesian近似计算算法，已经被引用1850次

具体详情请见其个人主页：https://www.york.ac.uk/maths/staff/wenyang-zhang/。

摘要：

This talk, based on the joint paper by Jia Chen, Degui Li, Lingling Wei and Wenyang Zhang, explores the homogeneity of coefficient functions in nonlinear models with functional coefficients, and identifies the semiparametric modelling structure. With initial kernel estimate of each coefficient function, we combine the classic hierarchical clustering method and a generalised version of the information criterion to estimate the number of clusters each of Which has the common functional coefficient and determine the indices within each cluster. To specify the semi-varying coefficient modelling framework, we further introduce a penalised local least squares method to determine zero coefficient, non-zero constant coefficients and functional coefficients varying with an index variable. Through the nonparametric kernel-based cluster analysis and the penalised approach, the number of unknown parametric and nonparametric components in the models can be substantially reduced and the aim of dimension reduction can be achieved. Under some regularity conditions, we establish the asymptotic properties for the proposed methods such as consistency of the homogeneity pursuit. Some numerical studies including simulation and two empirical applications are given to examine the finite-sample performance of our methods.