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Improved likelihood inference for discrete data

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  • A. C. Davison
  • D. A. S. Fraser
  • N. Reid

Abstract

Summary. Discrete data, particularly count and contingency table data, are typically analysed by using methods that are accurate to first order, such as normal approximations for maximum likelihood estimators. By contrast continuous data can quite generally be analysed by using third‐order procedures, with major improvements in accuracy and with intrinsic separation of information concerning parameter components. The paper extends these higher order results to discrete data, yielding a methodology that is widely applicable and accurate to second order. The extension can be described in terms of an approximating exponential model that is expressed in terms of a score variable. The development is outlined and the flexibility of the approach is illustrated by examples.

Suggested Citation

  • A. C. Davison & D. A. S. Fraser & N. Reid, 2006. "Improved likelihood inference for discrete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 495-508, June.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:3:p:495-508
    DOI: 10.1111/j.1467-9868.2006.00548.x
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    Cited by:

    1. Chris J. Lloyd, 2010. "Bootstrap and Second-Order Tests of Risk Difference," Biometrics, The International Biometric Society, vol. 66(3), pages 975-982, September.
    2. Ip, Edward H. & Wang, Yuchung J., 2008. "A note on cuts for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2356-2363, November.
    3. Donald Alan Pierce & Ruggero Bellio, 2017. "Modern Likelihood-Frequentist Inference," International Statistical Review, International Statistical Institute, vol. 85(3), pages 519-541, December.
    4. Rekkas, M., 2009. "Approximate inference for the multinomial logit model," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 237-242, January.
    5. Lloyd, Chris J., 2010. "How close are alternative bootstrap P-values?," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1972-1976, December.
    6. A. C. Davison & D. A. S. Fraser & N. Reid & N. Sartori, 2014. "Accurate Directional Inference for Vector Parameters in Linear Exponential Families," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 302-314, March.
    7. D. A. S. Fraser & N. Reid & E. Marras & G. Y. Yi, 2010. "Default priors for Bayesian and frequentist inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 631-654, November.
    8. Martin Biehler & Heinz Holling & Philipp Doebler, 2015. "Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 665-688, September.

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