报告题目：Nonparametric Inference for Partly Linear Additive Cox Models based on Polynomial Spline Estimation
                  
       主讲人：蒋建成教授（北卡罗莱纳大学夏洛特分校）
       时间：2019年7月3日（周三）9:00 a.m.
       地点：北院卓远楼305
       主办单位：统计与数学学院

       摘要：The global smoothing method based on polynomial splines is a popular technique for nonparametric regression estimation and has received great attention in the literature. However, it is tremendously challenging to obtain local asymptotic properties of the polynomial spline estimators and to make inference for the regression functions. We develop a general theory of local asymptotics for the polynomial spline estimation of partly linear additive Cox models. We obtain a uniform Bahadur representation of and design-adaptive asymptotic normality of the resulting nonparametric estimators. Furthermore, we propose a distance-based statistic for specification tests of the additive components and establish the limiting distribution of the test statistic. We propose a bootstrap procedure to calculate the p-value of the above test statistic and prove its consistency. Based on the polynomial-spline estimation, we also introduce a two-step estimation method, which possesses an oracle property in the sense that any additive component could be estimated as if other additive components were known. All of the above local asymptotics and testing results are also established for this two-step procedure. Simulations demonstrate nice finite sample performance of the proposed procedure. Analysis of the Framingham Heart Study data illustrates the use of our methodology.

       主讲人简介：
       蒋建成博士是北卡大学夏洛特分校的统计学教授。主要研究领域包括统计和计量经济学。发表科研论文58篇。曾获多项中美两国国家自然科学基金。现任Statistica Sinica，Frontiers in Artificial Intelligence和Journal of Testing and Evaluation等期刊的副主编。