On Hotelling's T2 test in a special paired sample case. Issue 2 (17th January 2019)

• Record Type: Journal Article
• Authors: Baringhaus, Ludwig; Gaigall, Daniel
• Is Part Of: Communications in statistics. Volume 48:Issue 2(2019)
• Page Start: 257
• Page End: 267
• Publication Date: 2019-01-17
• Subjects: complete block symmetry -- Hotelling's T2 test -- likelihood ratio test -- uniformly most powerful invariant test.; 62H15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1408828
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In a special paired sample case, Hotelling's T 2 test based on the differences of the paired random vectors is the likelihood ratio test for testing the hypothesis that the paired random vectors have the same mean; with respect to a special group of affine linear transformations it is the uniformly most powerful invariant test for the general alternative of a difference in mean. We present an elementary straightforward proof of this result. The likelihood ratio test for testing the hypothesis that the covariance structure is of the assumed special form is derived and discussed. Applications to real data are given.