课程：Smoothing Spline ANOVA Models（光滑样条方差分析模型）

时间：2015年6月18日，6月25日

课程网址：http:/academic/86227.html

地点：威尼斯wns885566沙河校区

2015年6月18日（星期四），10：10-12：00，19：00-20：50 沙河校区主教409

2015年6月25日（星期四），10：10-12：00，19：00-20：50 沙河校区主教309

（上机时间另行安排）

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 Ping Ma, Department of Statistics, University of Georgia

马平教授为威尼斯wns885566“手拉手”项目特聘教授，佐治亚大学（UGA）统计系副教授，美国普渡大学统计学博士，哈佛大学统计系博士后。马平教授在非参数统计、数据建模、超大样本统计等方面有着很深的理论造诣，在高水平学术杂志上发表论文20余篇，承担9项美国国家科学基金（NSF）科研项目。曾获得Canadian Journal of Statistics优秀论文奖、美国自然科学基金CAREER 奖。University of Illinois优秀教师，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

This course presents a systematic treatment of multivariate function estimation via the penalized likelihood method. Emphasis will be placed on the structural model construction, the selection of smoothing parameters, and the use of software tools. A tentative outline of coverage follows.

Introduction: Cubic smoothing spline; functional ANOVA decomposition; additive models.

Model construction: Reproducing kernel Hilbert space; shrinkage estimates; univariate splines; tensor product splines; empirical Bayes model.

Gaussian regression: Smoothing parameter selection and cross validation; Bayesian confidence intervals; cosine diagnostics; software tools.

Non-Gaussian regression: Smoothing parameter selection; Bayesian confidence intervals; software tools.

If time permits, some of the following topics may also be covered.

Probability density estimation: Logistic density transform; biased sampling and random truncation; conditional density estimation; smoothing parameter selection.

Some of the latest results and on-going research projects by your instructor and his students may also be discussed.

Software tools implementing some of the techniques discussed in this course have been developed in gss package under R. Working knowledge of statistical inference, linear models, generalized linear models, and matrix algebra. Prior knowledge of Hilbert space is helpful but not required.

参考文献

Smoothing Spline ANOVA Models Chong Gu (2013) 2nd Edition.

Spline Models for Observational Data, by Grace Wahba (1991).