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Predictive probability matching priors for a certain non-regular model

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  • Hashimoto, Shintaro

Abstract

Probability matching priors for Bayesian prediction in non-regular case are considered. For one-parameter family of distributions, the resulting priors match the posterior predictive quantile with the frequentist one up to the order of o(n−2), and they are solutions of a certain differential equation (denoted by matching equation). Although predictive probability matching priors depend on a nominal rate α in general, we provide a prior which satisfy the matching equation for every nominal rate α in non-regular location and scale models. A multi-parameter extension including location-scale model is also discussed.

Suggested Citation

  • Hashimoto, Shintaro, 2021. "Predictive probability matching priors for a certain non-regular model," Statistics & Probability Letters, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:stapro:v:174:y:2021:i:c:s0167715221000584
    DOI: 10.1016/j.spl.2021.109096
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    References listed on IDEAS

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    1. Subhashis Ghosal & Tapas Samanta, 1997. "Asymptotic Expansions of Posterior Distributions in Nonregular Cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 181-197, March.
    2. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, vol. 72(5), pages 1445-1480, September.
    3. S. Ghosal, 1997. "Reference priors in multiparameter nonregular cases," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 159-186, June.
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