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Asymptotic properties of a goodness-of-fit test based on maximum correlations

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  • Grané, Aurea
  • Tchirina, Anna V.

Abstract

We study the efficiency properties of the goodness-of-fit test based on the Qn statistic introduced in Fortiana and Grané (2003) 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 and the Anderson-Darling statistics. We also describe the distribution families for which the test based on Qn is 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.

Suggested Citation

  • Grané, Aurea & Tchirina, Anna V., 2008. "Asymptotic properties of a goodness-of-fit test based on maximum correlations," DES - Working Papers. Statistics and Econometrics. WS ws084211, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws084211
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    References listed on IDEAS

    as
    1. J. Fortiana & A. Grané, 2003. "Goodness‐of‐fit tests based on maximum correlations and their orthogonal decompositions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 115-126, February.
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    2. Aurea Grané, 2012. "Exact goodness-of-fit tests for censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1187-1203, December.
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    Keywords

    Bahadur asymptotic relative efficiency;

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