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December, 1956 Asymptotic Formulae for the Distribution of Hotelling's Generalized $T^2_0$ Statistic
Koichi Ito
Ann. Math. Statist. 27(4): 1091-1105 (December, 1956). DOI: 10.1214/aoms/1177728075


In this paper the asymptotic expansion of a percentage point of Hotelling's generalized $T^2_0$ distribution is derived in terms of the corresponding percentage point of a $\chi^2$ distribution. Our result generalizes Hotelling's and Frankel's asymptotic expansion for the generalized Student $T$ [3], [4]. The technique used in this paper for obtaining the asymptotic expansion of $T^2_0$ is an extension of the previous methods of Welch [8] and of James [5], [6], who used them to solve the distribution problem of various statistics in connection with the Behrens-Fisher problem. An asymptotic formula for the cumulative distribution function (c.d.f.) of $T^2_0$ is also given together with an upper bound for the error committed when all but the first few terms are omitted in the series. This formula is a sort of multivariate analogue of Hartley's formula of "Studentization" [2].


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Koichi Ito. "Asymptotic Formulae for the Distribution of Hotelling's Generalized $T^2_0$ Statistic." Ann. Math. Statist. 27 (4) 1091 - 1105, December, 1956.


Published: December, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0249.62050
MathSciNet: MR84969
Digital Object Identifier: 10.1214/aoms/1177728075

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 4 • December, 1956
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