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We study the efficiency properties of the goodness-of-fit test based on the Q n statistic introduced in Fortiana and Grane [Goodness-of-fit tests based on maximum correlations and their orthogonal decompositions, J. R. Stat. Soc. B 65 (2003), pp. 115126] using the concepts of Bahadur asymptotic relative efficiency and Bahadur asymptotic optimality. We compare the test based on this statistic with those based on the KolmogorovSmirnov, the Cramer-von Mises criterion and the AndersonDarling statistics. We also describe the distribution families for which the test based on Q n is locally asymptotically optimal in the Bahadur sense and, as an application, we use this test to detect the presence of hidden periodicities in a stationary time series.
bahadur asymptotic relative efficiency; goodness-of-fit; local asymptotic optimality; l-statistics; maximum correlation