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题目： A Lack-of-fit Test with Screening in Sufficient Dimension Reduction for Ultrahigh Dimensional Data

报告人：朱利平 教授 （中国人民大学）

摘要: It is of fundamental importance to infer how the conditional mean of the response varies with the predictors in high dimensional data analysis. Sufficient dimension reduction techniques reduce the dimension by identifying a minimal set of linear combinations of the original predictors without loss of information. This paper is concerned with testing whether a given small number of linear combinations of the original high dimensional covariates is sufficient to characterize the conditional mean of the response. To this end, we introduce a two-stagelack-of-fit test with screening (LOFTS) procedure based on data splitting strategy for ultrahigh dimensional data. We first randomly partition data into two equal halves. In the first screening stage, we apply the martingale difference correlation based screening to one half of the data and select a moderate set of covariates. In the second test stage, we propose a novel consistent lack-of-fit teststatistic based on the selected covariates and perform this test in the second half of the data. The proposed test is shown to be n-consistent under the null and root-n-consistent under the alternative hypothesis. A consistent bootstrap procedure is also proposed to approximate the p-values. The data splitting strategy is very crucial here to eliminate the effect of spurious correlations and avoid  the inflation of Type-I error rates of the proposed test. We also introduce a multiple splitting strategy which helps our proposed test to well maintain the empirical type-I error rates even when some important predictors are missed with a nonignorable probability. We demonstrate the effectiveness of our two-stage test procedure through comprehensive simulations and two real-data applications.

时间：11月11日（周五）下午3点-4点

地点：首都师范大学北一区文科楼505教室

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