Goodness-of-Fit Tests Based on Characterization of Uniformity by the Ratio of Order Statistics, and Their Efficiency

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We construct integral and supremum type goodness-of-fit tests for the uniform law based on Ahsanullah’s characterization of the uniform law. We discuss limiting distributions of new tests and describe the logarithmic large deviation asymptotics of test statistics under null-hypothesis. This enables us to calculate their local Bahadur efficiency under some parametric alternatives. Conditions of local optimality of new statistics are given.

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Correspondence to K. Yu. Volkova.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 67–80.

Translated by S. Yu. Pilyugin.

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Volkova, K.Y., Karakulov, M.S. & Nikitin, Y.Y. Goodness-of-Fit Tests Based on Characterization of Uniformity by the Ratio of Order Statistics, and Their Efficiency. J Math Sci 244, 743–751 (2020) doi:10.1007/s10958-020-04647-x

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