Open Access
Translator Disclaimer
March, 1994 Extremal Probabilistic Problems and Hotelling's $T^2$ Test Under a Symmetry Condition
Iosif Pinelis
Ann. Statist. 22(1): 357-368 (March, 1994). DOI: 10.1214/aos/1176325373


We consider the Hotelling $T^2$ statistic for an arbitrary $d$-dimensional sample. If the sampling is not too deterministic or inhomogeneous, then under the zero-means hypothesis the limiting distribution for $T^2$ is $\chi^2_d$. It is shown that a test for the orthant symmetry condition introduced by Efron can be constructed which does not differ essentially from the one based on $\chi^2_d$ and at the same time is applicable not only to large random homogeneous samples but to all multidimensional samples. The main results are not limit theorems, but exact inequalities corresponding to the solutions to certain extremal problems. The following auxiliary result itself may be of interest: $\chi_d - \sqrt{d - 1}$ has a monotone likelihood ratio.


Download Citation

Iosif Pinelis. "Extremal Probabilistic Problems and Hotelling's $T^2$ Test Under a Symmetry Condition." Ann. Statist. 22 (1) 357 - 368, March, 1994.


Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0812.62065
MathSciNet: MR1272088
Digital Object Identifier: 10.1214/aos/1176325373

Primary: 62H15
Secondary: 60E15, 62F04, 62F35, 62G10, 62G15

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • March, 1994
Back to Top