主讲人：美国加州大学圣巴巴拉分校统计与应用概率系 Yuedong Wang教授
主题：Smoothing Spline Semi-parametric Nonlinear Regression Models
主持人：林华珍教授
时 间：2013年7月11日上午11:00-12:00
地 点：通博楼B212会议室
主办：统计学院科研处
摘 要：
We consider the problem of modeling the mean function in regression. Often there is enough knowledge to model some components of the mean function parametrically. But for other vague and/or nuisance components, it is often desirable to leave them unspecified and to be modeled nonparametrically. We present a general class of smoothing spline semi-parametric nonlinear regression models (SNRM) which assumes that the mean function depends on parameters and nonparametric functions through a known nonlinear functional. SNRMs are natural extensions of both parametric and nonparametric regression models. They include many popular nonparametric and semi-parametric models such as the partial spline, varying coefficients, projection pursuit, single index, multiple index and shape invariant models as special cases. Building on reproducing kernel Hilbert spaces, the SNRMs allow us to deal with many different situations in a unified fashion. We develop a unified estimation procedure based on minimizing penalized likelihood using Gauss-Newton and backfitting algorithms. Smoothing parameters are estimated using the generalized cross-validation and generalized maximum likelihood methods. We derive Bayesian confidence intervals for the unknown functions. A generic and user-friendly R function is developed to implement our estimation and inference procedures. We illustrate our methods with analyses of real data sets and evaluate finite-sample performance by simulations.
主讲人介绍：
Yuedong Wang, 美国加州大学圣巴巴拉分校统计与应用概率系教授，主要研究领域包括生物统计建模，bootstrap, 广义线性模型，纵向数据分析，基因序列数据分析，混合效用模型，模型选择，生存分析等，在包括JASA等顶尖杂志发表论文60余篇。主讲人详细介绍请参看http://www.pstat.ucsb.edu/faculty/yuedong/CV.pdf
