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On approximations of transformed chi-squared distributions in statistical applications

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Abstract

We obtain some computable error bounds of order O(n −1) for the chi-squared approximation of transformed chi-squared random variables with n degrees of freedom. The results are applied to likelihood ratio statistics in the multivariate case.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. V. Ulyanov

  2. Institut für Mathematische Stochastik, Magdeburg, Deutschland

    G. Christoph

  3. Chuo University, Tokyo, Japan

    Y. Fujikoshi

Authors
  1. V. V. Ulyanov
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  2. G. Christoph
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  3. Y. Fujikoshi
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Original Russian Text Copyright © 2006 Ulyanov V. V., Christoph G., and Fujikoshi Y.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 6, pp. 1401–1413, November–December, 2006.

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Ulyanov, V.V., Christoph, G. & Fujikoshi, Y. On approximations of transformed chi-squared distributions in statistical applications. Sib Math J 47, 1154–1166 (2006). https://doi.org/10.1007/s11202-006-0121-7

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  • DOI: https://doi.org/10.1007/s11202-006-0121-7

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