课程：Non/semi--parametric modeling and related topics （非参数半参数模型及相关主题）

时间：2015年5月28日，5月30日

2015年5月28日（星期四），10：10-12：00，19：00-20：50 沙河校区主教309

2015年5月30日（星期六），09：00-12：00，14：00-17：00 沙河校区主教309

（上机时间另行安排）

课程网址： http://sam.cufe.edu.cn/academic/85742.html

地点：威斯尼斯人沙河校区

面向对象：课程面向国内各高校研究生、青年教师免费开放，食宿自理。短期课程参与者不需要报名，按时间前来听课即可。有关于课程的任何问题请联系李丰老师（电子邮件feng.li@cufe.edu.cn）

学时：12学时

教师：Professor Hua Liang, Department of Statistics, The George Washington University

梁华教授为威斯尼斯人统计与数学学院“手拉手”项目特聘教授，美国乔治华盛顿大学教授，中科院数理统计博士，Texas A&M University统计学博士。出版学术著作2部, 学术论文120多篇，其中20篇发表在国际统计学最顶级的四个期刊上（The Annals of Statistics, Biometrika, JASA, and JRSSB)。梁华教授共主持了6项美国国家科学基金会以及美国国立卫生研究院的研究项目，研究经费总计250万美元。另外还主持了1项海外港澳学者研究基金。他是美国统计学会(ASA), 国际数理统计学会(IMS), 英国皇家统计学会(RSS)会员。同时担任Journal of the American Statistical Association等多个国际著名统计学期刊的副主编。

课程内容

Topic 1 Techniques for Nonparametric Models

Nonparametric regression models have been used to explore the complicated relation between the response and the predictors of interest because it may be very difficult if not impossible to give any close- form to express this relationship. I will present an up--to--date picture on the state of nonparametric regression. Several fundamental techniques such as local polynomial, smoothing spline, and penalized spline will be presented.

Topic 2 Semi-parametric Generalized Partially Linear Models

More recently a lot of efforts have been made to balance the interpretability and simplicity of para-metric models and the flexibility of nonparametric models. Important results of those efforts are semi-parametric regression models. Emphasis in this lecture is on generalized partially linear models (GPLM), in which the conditional expectation of the response variable given covariates depends on some variable in a linear way but nonlinearly related to other variable. They compromise the interpretation of traditional (generalized) linear models and flexibility of non-parametric regression. GPLM contain generalizations of multiple linear regression models, generalized linear models, and partially linear models. This lecture will cover the methodological aspects of profile likelihood and backfitting in GPLM for cross--sectional and longitudinal data.

Topic 3 Generalized additive partial linear models

Concerning on the computational burden when backfitting and kernel methods are used to fit generalized additive partial linear models (GAPLM), we have made a lot of efforts for use of spline to approximate nonparametric functions and to make inference in GAPLM. This lecture will cover estimation and inference in GAPLM for cross-section and correlated data using the generalized estimating equation and quadratic inference function principles.

主要参考文献

Fan, J. and Gijbels, I. (1996).Local Polynomial Modelling and Its Applications.Vol. 66 of Monographs on Statistics and Applied Probability, Chapman and Hall, New York.

Haerdle, W., Liang, H. and Gao, J. (2000). Partially Linear Models.Springer Physica-Verlag, Heidelberg.

Hastie, T. J. and Tibshirani, R. J. (1990).Generalized Additive Models, Vol. 43 of Mono-graphs on Statistics and Applied Probability, Chapman and Hall, London.

[编辑]：孙颖