Open AccessTwo new multivariate tests, in particular for a high dimension
Author(s) -
Jürgen Läuter
Publication year - 2004
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2004.08.13
Subject(s) - dimension (graph theory) , multivariate statistics , null hypothesis , statistics , principal component analysis , sample size determination , mathematics
Two new test statistics for the multivariate one-sample problem are introduced that are applicable to normally distributed data in all cases with a sample size n≥2 and a dimension p≥1. The dimension may also be greater than the sample size. The tests are based on the theory of spherical distributions. They utilize the principal components of the total sums of product matrices of the given data. Under the null hypothesis, the statistics are exactly beta distributed. The performance of the tests is investigated by simulations. Finally, the methods are applied to high-dimensional data from gene expression analysis (dimension p=12625).