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Karhunen-loève basis in goodness-of-fit tests decomposition: an evaluation

Listed author(s):
  • Fortiana, Josep
  • Grané, Aurea
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    In a previous paper (Grané and Fortiana 2006) we studied a flexible class of goodness-of-fit tests associated with an orthogonal sequence, the Karhunen-Loève decomposition of a stochastic process derived from the null hypothesis. Generally speaking, these tests outperform Kolmogorov-Smirnov and Cramér-von Mises, but we registered several exceptions. In this work we investigate the cause of these anomalies and, more precisely, whether and when such poor behaviour may be attributed to the orthogonal sequence itself, by replacing it with the Legendre polynomials, a commonly used basis for smooth tests. We find an easily computable formula for the Bahadur asymptotic relative efficiency, a helpful quantity in choosing an adequate basis.

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    Paper provided by Universidad Carlos III de Madrid. Departamento de Estadística in its series DES - Working Papers. Statistics and Econometrics. WS with number ws062710.

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    Date of creation: Apr 2006
    Handle: RePEc:cte:wsrepe:ws062710
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    1. Cuadras, C. M. & Fortiana, J., 1995. "A Continuous Metric Scaling Solution for a Random Variable," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 1-14, January.
    2. 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.
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