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Use of the Gibbs Sampler to Obtain Conditional Tests, with Applications

Author

Listed:
  • Richard A. Lockhart
  • Federico J. O'Reilly
  • Michael A. Stephens

Abstract

A random sample is drawn from a distribution which admits a minimal sufficient statistic for the parameters. The Gibbs sampler is proposed to generate samples, called conditionally sufficient or co-sufficient samples, from the conditional distribution of the sample given its value of the sufficient statistic. The procedure is illustrated for the gamma distribution. Co-sufficient samples may be used to give exact tests of fit; for the gamma distribution these are compared for size and power with approximate tests based on the parametric bootstrap. Copyright 2007, Oxford University Press.

Suggested Citation

  • Richard A. Lockhart & Federico J. O'Reilly & Michael A. Stephens, 2007. "Use of the Gibbs Sampler to Obtain Conditional Tests, with Applications," Biometrika, Biometrika Trust, vol. 94(4), pages 992-998.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:4:p:992-998
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    File URL: http://hdl.handle.net/10.1093/biomet/asm065
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    Citations

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    Cited by:

    1. José González-Barrios & Federico O’Reilly & Raúl Rueda, 2010. "Durbin’s random substitution and conditional Monte Carlo," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 369-383, November.
    2. Villaseñor, José A. & González-Estrada, Elizabeth, 2015. "A variance ratio test of fit for Gamma distributions," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 281-286.
    3. J. I. Beltrán-Beltrán & F. J. O’Reilly, 2019. "On goodness of fit tests for the Poisson, negative binomial and binomial distributions," Statistical Papers, Springer, vol. 60(1), pages 1-18, February.
    4. Bo H. Lindqvist & Rasmus Erlemann & Gunnar Taraldsen, 2022. "Conditional Monte Carlo revisited," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 943-968, September.
    5. Michael A. Stephens, 2012. "Goodness-of-Fit and Sufficiency: Exact and Approximate Tests," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 785-791, September.

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