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 Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 67–80 (Mi znsl6541)

Goodness-of-fit tests based on the characterization of uniformity by the ratio of order statistics, and their efficiencies

K. Yu. Volkova, M. S. Karakulov, Ya. Yu. Nikitin

St. Petersburg State University, St. Petersburg, Russia

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

Key words and phrases: uniform distribution, hypotheses testing, characterization, $U$-statistics, large deviations, Bahadur efficiency, local optimality.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00258 Saint Petersburg State University ÑÏáÃÓ-DFG 6.65.37.2017

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Document Type: Article
UDC: 519.2

Citation: K. Yu. Volkova, M. S. Karakulov, Ya. Yu. Nikitin, “Goodness-of-fit tests based on the characterization of uniformity by the ratio of order statistics, and their efficiencies”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 67–80

Citation in format AMSBIB
\Bibitem{VolKarNik17} \by K.~Yu.~Volkova, M.~S.~Karakulov, Ya.~Yu.~Nikitin \paper Goodness-of-fit tests based on the characterization of uniformity by the ratio of order statistics, and their efficiencies \inbook Probability and statistics. Part~26 \serial Zap. Nauchn. Sem. POMI \yr 2017 \vol 466 \pages 67--80 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6541}