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An Everywhere Convergent Series Representation of the Distribution of Hotelling's Generalized T_{0}^{2}

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Abstract

A new series representation of the exact distribution of Hotelling's generalized T_{0}^{2}statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the noncentral distributions. Earlier results by Constantine [1], which are convergent on the interval [0,1), are also derived quite simply from our formulae.

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  • Peter C.B. Phillips, 1983. "An Everywhere Convergent Series Representation of the Distribution of Hotelling's Generalized T_{0}^{2}," Cowles Foundation Discussion Papers 723R, Cowles Foundation for Research in Economics, Yale University, revised Mar 1986.
    • Handle: RePEc:cwl:cwldpp:723r
    Note: CFP 675.
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    1. Pillai, K. C. S. & Young, D. L., 1971. "On the exact distribution of Hotelling's generalized," Journal of Multivariate Analysis, Elsevier, vol. 1(1), pages 90-107, April.
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    1. Peter C.B. Phillips, 1985. "Fractional Matrix Calculus and the Distribution of Multivariate Tests," Cowles Foundation Discussion Papers 767, Cowles Foundation for Research in Economics, Yale University.

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