Asymptotic properties of a goodness-of-fit test based on maximum correlations |
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Authors: | Aurea Grané Anna V Tchirina |
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Institution: | 1. Statistics Department , Universidad Carlos III de Madrid , C/ Madrid 126, 28903 , Getafe , Spain aurea.grane@uc3m.es;3. St Petersburg Electrotechnical University , St Petersburg , Russian Federation |
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Abstract: | We study the efficiency properties of the goodness-of-fit test based on the Q n statistic introduced in Fortiana and Grané Goodness-of-fit tests based on maximum correlations and their orthogonal decompositions, J. R. Stat. Soc. B 65 (2003), pp. 115–126] 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 Kolmogorov–Smirnov, the Cramér-von Mises criterion and the Anderson–Darling 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. |
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Keywords: | Bahadur asymptotic relative efficiency goodness-of-fit local asymptotic optimality L-statistics maximum correlation |
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