题  目：A Lack-of-Fit Test for Generalized Linear Models with Ultrahigh Dimensional Covariates

主讲人：周亭攸

主持人：罗季教授

时  间：2017年11月1日（周三）14：45-15：45

地  点：6号学院楼402会议室

主讲人简介：

周亭攸，女，1990年生，2017年毕业于上海财经大学统计与管理学院，博士学位。现任职于yh86银河国际，讲师。长期从事统计学理论和方法研究，研究方向集中在高维及超高维数据统计分析、半参数回归模型统计推断等领域。

摘  要：

We propose a modified two-stage test for the GLM model-check when the number of covariates p is much larger than the sample size n. Specifically, we randomly split the whole data set into two equal halves D_1 and D_2. In the first stage, we carry out a screening procedure to select some active variables based on D_1. Then in the second stage, we propose a lack-of-fit test based on the selected variables using dataset D_2. Our method can avoid potential type-I error inflation and power loss, which are widely existed when p>>n. A novel test statistic, which is n-consistent under the null and root-n-consistent under the alternative, is put forward and a consistent bootstrap procedure is suggested to decide critical value. Our proposal is not only powerful against the global alternative, but also detectable for local alternatives at the rate of order n^{-1/2}. We further demonstrate the usefulness of our proposal through an analysis of the cardiomyopathy microarray data.

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