Summary
Let \(\mathfrak{F}_p (\mathfrak{F}_n )\) be the class of all two dimensional continuous distributions with positive (negative) likelihood ratio dependence. It is shown that the Pitman permutation test for testing independence against positive likelihood ratio dependence at level α is unbiased and of level α for \(\mathfrak{F}_n \). Furthermore, it is optimal against the class of normal distributions with positive correlation coefficient ρ.
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Lehmann, E. L.: Testing statistical hypotheses. New York: Wiley 1959.
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Pitman, E. J. G.: Significance tests which may be applied to samples from any population. J. roy. statist. Soc. Suppl. 4, 225–232 (1937).
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Herr Dr. G. Nölle ist am 20. 7. 1968 verstorben.
Herrn Professor Dr.H. Witting, Munster, danken wir flür RatschlÄge und Hinweise bei der Fertigsteliung dieser Arbeit.
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Neuhaus, G., Nölle, G. Zur UnverfÄlschtheit des Pitman-Tests auf positive stochastische AbhÄngigkeit. Z. Wahrscheinlichkeitstheorie verw Gebiete 14, 269–274 (1970). https://doi.org/10.1007/BF00533665
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DOI: https://doi.org/10.1007/BF00533665