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Bahadur asymptotic efficiency of ω2 -type tests in the many-sample case

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Abstract

Consider

independent samples of sizen 1,n 2,... ,n 2 and the empirical distribtion

constructed using these samples. We test the hypothesis that all the samples are drawn from a population with the same continuous distribution function F (x). The test statistic

is the weight function) is defined as

generalizes Kiefer's well-known statistic originally proposed for the case K=2 and q,= 1. A rough asymptotics is obtained for the probability of large deviations of the statistic

, which allows to give explicit expressions for the Bahadur local exact slopes and to compare the statistics for various K and q in the sense of Bahadur efficiency. In conclusion, the question posed by Renyi is considered: to what extent is it advisable to use statistics of the type

instead of pooling all the samples and using a one-sample test?

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Literature cited

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Authors
  1. Ya. Yu. Nikitin
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Additional information

Translated from Zapiski Nauchnykh Seminatov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 98, pp. 140–148, 1980.

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Nikitin, Y.Y. Bahadur asymptotic efficiency of ω2 -type tests in the many-sample case. J Math Sci 21, 93–99 (1983). https://doi.org/10.1007/BF01091459

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  • DOI: https://doi.org/10.1007/BF01091459

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