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Bayesian shrinkage estimation of negative multinomial parameter vectors

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  • Hamura, Yasuyuki
  • Kubokawa, Tatsuya

Abstract

The negative multinomial distribution is a multivariate generalization of the negative binomial distribution. In this paper, we consider the problem of estimating an unknown matrix of probabilities on the basis of observations of negative multinomial variables under the standardized squared error loss. First, a general sufficient condition for a shrinkage estimator to dominate the UMVU estimator is derived and an empirical Bayes estimator satisfying the condition is constructed. Next, a hierarchical shrinkage prior is introduced, an associated Bayes estimator is shown to dominate the UMVU estimator under some conditions, and some remarks about posterior computation are presented. Finally, shrinkage estimators and the UMVU estimator are compared by simulation.

Suggested Citation

  • Hamura, Yasuyuki & Kubokawa, Tatsuya, 2020. "Bayesian shrinkage estimation of negative multinomial parameter vectors," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x20302347
    DOI: 10.1016/j.jmva.2020.104653
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    References listed on IDEAS

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    1. Komaki, Fumiyasu, 2006. "A class of proper priors for Bayesian simultaneous prediction of independent Poisson observables," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1815-1828, September.
    2. Ghosh, Malay & Parsian, Ahmad, 1981. "Bayes minimax estimation of multiple Poisson parameters," Journal of Multivariate Analysis, Elsevier, vol. 11(2), pages 280-288, June.
    3. Komaki, Fumiyasu, 2015. "Simultaneous prediction for independent Poisson processes with different durations," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 35-48.
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