Open Access
December, 1960 Asymptotic Formulae for the Distribution of Hotelling's Generalized $T_0^2$ Statistic. II
Koichi Ito
Ann. Math. Statist. 31(4): 1148-1153 (December, 1960). DOI: 10.1214/aoms/1177705685


In this paper an asymptotic formula for the cumulative distribution function (c.d.f.) of Hotelling's generalized $T_0^2$ statistic is derived for general values of the number of dimensions in the non-null case. This result includes as a special case the previous result of the author for the null distribution of $T_0^2$ [5], and shows certain properties of $T_0^2$ which help determine the power of the test based on the statistic for moderately large samples. Both of the author's results provide an approximate complete analysis of the $T_0^2$ test, although the exact null and non-null distributions of $T_0^2$ are not available at present.


Download Citation

Koichi Ito. "Asymptotic Formulae for the Distribution of Hotelling's Generalized $T_0^2$ Statistic. II." Ann. Math. Statist. 31 (4) 1148 - 1153, December, 1960.


Published: December, 1960
First available in Project Euclid: 27 April 2007

zbMATH: 0249.62050
MathSciNet: MR116401
Digital Object Identifier: 10.1214/aoms/1177705685

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 4 • December, 1960
Back to Top