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

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

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...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-02, Vol.244 (5), p.743-751
Hauptverfasser: Volkova, K. Yu, Karakulov, M. S., Nikitin, Ya. Yu
Format: Artikel
Sprache:eng
Schlagworte:
Goodness of fit
Mathematics
Mathematics and Statistics
Statistical tests
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Zusammenfassung: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04647-x