讲座编号：jz-yjsb-2015-y080

讲座问题：Jackknife Empirical Likelihood Goodness-Of-Fit Tests For U-Statistics Based General Estimating Equations

主 讲 人：彭翰湘 教授 美国印第安纳大学与普渡大学印第安纳波里斯团结分校（IUPUI）

讲座时间：2015年11月09日（星期一）下昼15:00

讲座所在：阜成路东校区一号楼241室

加入工具：理学院统计专业的青年西席及研究生

主理单位：理学院

主讲人简介：

彭翰湘：博士，美国印第安纳大学与普渡大学印第安纳波里斯团结分校（IUPUI）数学科学学院教授，博士生导师，曾任美国密西西比大学数学系教授。主要研究领域有：

(1) 生涯剖析: 由自由结点样条探索危害回合并研究其渐进性在康健科学领域的应用；

(2) 相关数据模子和广义线性模子；

(3) 半参数回归: 

(4) 稳健统计:

(5) 履历似然

主讲内容：

Motivated by applications to goodness of fit U-statistic testing,the jackknife empirical likelihood (JEL) for U-statistics (Jing, sl et al. (2009)) is justified with two alternative approaches and the Wilks theorems are proved. This generalizes empirical likelihood for general estimating equations to U-statistics based general estimating equations (UGEE). The results are extended to allow for the constraints to use estimated functions and for the number of constraints to grow with the increasing sample size. It is exhibited that the JEL can be used to conveniently construct empirical likelihood tests for many commonly used moment based distribution characteristics with less computational burden and more flexibility than the usual empirical likelihood.  This can be done by two approaches, i.e. the U-statistics representation approach and the vector U-statistics approach. Such characteristics include Cohen's kappa, concordance correlation coefficient, coefficient of variation, Cronbach's coefficient alpha, Goodman &Kruskal's Gamma, interclass correlation, Kendall's taub, Pearson's correlation, skewness and kurtosis, U-quantiles (taking as U-medians Hodges-Lehmann's median, Gini's mean difference and Theil's test), and the simplicial depth function. JEL tests are also constructed for UGEE for linear mixed effects models, for a balanced one-way random effects model, for overdisperson models, and for zero-inflated Poisson models. These tests are incorporated with an finite number and/or growing number of constraints and asymptotically distribution free. Simulations are run to evaluate these tests and to exhibit their power improvement with incorporation of side information.