A Graphical Dimension-reduction Technique for Testing Normal Goodness-of-fit of Multivariate Data
主 题: A Graphical Dimension-reduction Technique for Testing Normal Goodness-of-fit of Multivariate Data
报告人: Dr. Liang,Jia-Juan (University of New Haven, U.S.A.)
时 间: 2007-06-19 上午 10:30 - 11:30
地 点: 理科一号楼 1490
The multivariate normal assumption is commonly imposed on statistical models for analysis of multivariate data. Testing such an assumption is simply called testing multinormality or normal goodness-of-fit in the literature. There are various existing methods for this purpose. Unfortunately, most existing methods were derived from the large-sample theory that may require huge sample sizes for high-dimensional cases, or their power could be easily influenced by the curse of dimensionality. In this paper we will develop a graphical dimension-reduction technique to detect the evidence of potential violation of the multivariate normal assumption in analysis of high-dimensional data. The idea for dimension reduction is based on the principal components and the properties of spherical distributions. With the help of the dimension-reduction technique, high-dimensional sample data are projected onto some sample principal component directions and existing graphical techniques for detecting univariate normality can be applied to each principal component direction. As a result, detecting multivariate normality can be carried out by combining the sample information from each principal component. A
Monte Carlo study demonstrates the performance of the proposed method. Application of the new method is illustrated by real data sets.
