题目：Principal Component Tests for both Parametric and Nonparametric Statistical Analysis

报告人：Prof. Jiajuan Liang（University of New Haven）

摘要：The principal component (PC) approach is often used to collect sample information in high-dimensional data analysis. The PC-directions resulted from the eigenvalue-eigenvector problem in PC analysis usually act as dimension-reduction through projecting high-dimensional data onto the PC-directions. This idea can be applied to constructing parametric tests for the high-dimensional normal mean and the comparisons among several high-dimensional normal means. The PC-type parametric tests can be extended to testing the mean of a family of spherical distributions. The same idea can be applied to constructing projection-type goodness-of-fit tests for multinormality and constructing graphical tests for detecting non-multinormality. The noticeable property of the PC-tests is their applicability for the cases of both high and low dimension with small sample sizes. Even if the sample size is smaller than the dimension of the sample data when classical tests for the same purpose are no longer applicable, the PC-tests still perform well. As a result, the PC-tests outperform the classical tests for the same purpose in the case of high dimension with a sample size. Some Monte Carlo study is presented to demonstrate the effectiveness of the PC-tests for both parametric and nonparametric data analysis.  Some real-data examples are illustrated by using the PC-tests.

时间：7月11日（周六）上午10:30-11:30

地点：350vip葡京新集团登入网址北一区文科楼 708 教室

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