蔡天文 Tony Cai 2014-10-10 6:14 PM

High-Dimensional Sparse MANOVA

Abstract

This paper considers testing the equality of multiple high-dimensional mean vectors under dependency. We propose a test that is based on a linear transformation of the data by the precision matrix which incorporates the dependence structure of the variables. The limiting null distribution of the test statistic is derived and is shown to be the extreme value distribution of type I. The convergence to the limiting distribution is, however, slow when the number of groups is relatively large. An intermediate correction factor is introduced which significantly improves the accuracy of the test. It is shown that the test is particularly powerful against sparse alternatives and enjoys certain optimality. A simulation study is carried out to examine the numerical performance of the test and compare with other tests given in the literature. The numerical results show that the proposed test significantly outperforms those tests against sparse alternatives.


Full Article

KEYWORDS

SHARE & LIKE

COMMENTS

ABOUT THE AUTHOR

蔡天文 Tony Cai

宾夕法尼亚大学沃顿商学院Dorothy Silberberg 统计学讲席教授、应用数学及计算科学教授

0 Following 12 Fans 0 Projects 7 Articles

SIMILAR ARTICLES

AbstractPrincipal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications.This paper conside

Read More

AbstractEstimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one proj

Read More

AbstractIt is often of interest to understand how the structure of a genetic network differs between two conditions. In this paper, each condition-spec

Read More

AbstractThis paper considers testing the equality of multiple high-dimensional mean vectors under dependency. We propose a test that is based on a line

Read More

AbstractPrincipal component analysis (PCA) is one of the most commonly used statistical procedures for dimension reduction. This paper presents some re

Read More

AbstractThis paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in ℜp as the number

Read More

AbstractTolerance intervals are widely used in industrial applications. So far attention has been mainly focused on the construction of tolerance inter

Read More