A class of goodness-of-fit tests for circular distributions based on trigonometric moments

• Sreenivasa Rao Jammalamadaka ^[1] ; M. Dolores Jiménez-Gamero ^[2] ; Simos G. Meintanis ^[3]
  1. [1] University of California, Santa Barbara

     University of California, Santa Barbara

     Estados Unidos

     
  2. [2] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
  3. [3] National and Kapodistrian University of Athens

     National and Kapodistrian University of Athens

     Dimos Athens, Grecia

     

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• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 43, Nº. 2, 2019, págs. 317-336
• Idioma: inglés
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• Resumen

  • We propose a class of goodness–of–fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure.