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Orthogonal expansions for the generalized Cramér-von Mises statistics

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Abstract.

We provide a new proof for the representation of Cramér-von Mises statistics under (known) gamma and normal distributions. The new method uses orthogonal polynomials and provides an explicit form of the statistics from which the asymptotic distribution can be calculated.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa Tarfia, s/n, Universidad de Sevilla, 41012, Sevilla, Spain

    Fernando López-Blázquez

  2. Departamento de Estadística e Investigación Operativa Porvera, Universidad de Cádiz, 54 11401, Jerez de la Frontera (Cádiz), Spain

    Antonia Castaño-Martínez

Authors
  1. Fernando López-Blázquez
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  2. Antonia Castaño-Martínez
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Corresponding author

Correspondence to Antonia Castaño-Martínez.

Additional information

Acknowledgements This research was partially supported by FQM-331, FQM-270, BMF 2001-2378 and BMF2002-04525-C02-02. The authors are thankful to the referees for their suggestions and helpful comments.

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López-Blázquez, F., Castaño-Martínez, A. Orthogonal expansions for the generalized Cramér-von Mises statistics. Metrika 60, 211–221 (2004). https://doi.org/10.1007/s001840300304

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  • DOI: https://doi.org/10.1007/s001840300304

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