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Minimax character of the complex analog of the T2-test

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Abstract

In this paper we investigate the minimax properties of the complex analog of the T2-test, introduced by Giri for Goodman's complex normal multi-dimensional model. For the simplest non-trivial case, p = 2, N = 3, it is proven that this test maximizes, among all the tests of α, the minimal power over the set of alternatives. The bibliography contains seven titles.

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Literature cited

  1. N. R. Goodman, Statistical analysis on a certain multivariate complex Gaussian distribution (an introduction), Ann. Math. Statistics,34, No. 1, 152–177 (1963).

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  2. N. Giri, On the complex analogs of T2- and R2-tests. Ann. Math. Statistics,36, No. 2, 664–670 (1965).

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  3. N. Giri, J. Kiefer, and C. Stein, Minimax character of Hotteling's T2-test in the simplest case, Ann. Math. Statistics,34, No. 4, 1524–1535 (1963).

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  4. É. Leman, Testing Statistical Hypotheses [in Russian], Moscow (1964).

  5. Yu. V. Iinnik, V. A. Pliss, and O. V. Shalaevskii, On the Theory of Hotteling's Test, Dokl. AN SSSR,168, No. 4, 743–746 (1966).

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  6. E. L. Ince, Ordinary Differential Equations [Russian translation], Kharkov (1939).

  7. F. R. Gantmakher, Matrix Theory [in Russian], Moscow (1966).

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Authors and Affiliations

  1. Leningrad Section, V. A. Steklov Mathematical Institute of the Academy of Sciences of the USSR, USSR

    N. M. Khalfina

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  1. N. M. Khalfina
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Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 635–644, December, 1967.

The author wishes to thank Yu. V. Linnik for having posed the problem and O. V. Shalaevskii for his discussions of the work.

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Khalfina, N.M. Minimax character of the complex analog of the T2-test. Mathematical Notes of the Academy of Sciences of the USSR 2, 875–880 (1967). https://doi.org/10.1007/BF01473470

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