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Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure

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  • Luai Al Labadi
  • Mahmoud Zarepour

Abstract

The Dirichlet process is a fundamental tool in studying Bayesian nonparametric inference. The Dirichlet process has several sum representations, where each one of these representations highlights some aspects of this important process. In this paper, we use the sum representations of the Dirichlet process to derive explicit expressions that are used to calculate Kolmogorov, Lévy, and Cramér-von Mises distances between the Dirichlet process and its base measure. The derived expressions of the distance are used to select a proper value for the concentration parameter of the Dirichlet process. These tools are also used in a goodness-of-fit test. Illustrative examples and simulation results are included.

Suggested Citation

  • Luai Al Labadi & Mahmoud Zarepour, 2014. "Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 341-357, June.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:341-357
    DOI: 10.1080/10485252.2013.856431
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    1. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 105-120, March.
    2. Berger J. O & Guglielmi A., 2001. "Bayesian and Conditional Frequentist Testing of a Parametric Model Versus Nonparametric Alternatives," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 174-184, March.
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    Cited by:

    1. Rafael Carvalho Ceregatti & Rafael Izbicki & Luis Ernesto Bueno Salasar, 2021. "WIKS: a general Bayesian nonparametric index for quantifying differences between two populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 274-291, March.
    2. Luai Al Labadi & Ibrahim Abdelrazeq, 2017. "On functional central limit theorems of Bayesian nonparametric priors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 215-229, June.
    3. Luai Al Labadi & Mahmoud Zarepour, 2018. "On Approximations of the Beta Process in Latent Feature Models: Point Processes Approach," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 59-79, February.

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