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Objective Bayesian testing on the common mean of several normal distributions under divergence-based priors

Author

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  • Sang Gil Kang

    (Sangji University)

  • Woo Dong Lee

    (Daegu Haany University)

  • Yongku Kim

    (Kyungpook National University)

Abstract

This paper considers the problem of testing on the common mean of several normal distributions. We propose a solution based on a Bayesian model selection procedure in which no subjective input is considered. We construct the proper priors for testing hypotheses about the common mean based on measures of divergence between competing models. This method is called the divergence-based priors (Bayarri and García-Donato in J R Stat Soc B 70:981–1003, 2008). The behavior of the Bayes factors based DB priors is compared with the fractional Bayes factor in a simulation study and compared with the existing tests in two real examples.

Suggested Citation

  • Sang Gil Kang & Woo Dong Lee & Yongku Kim, 2017. "Objective Bayesian testing on the common mean of several normal distributions under divergence-based priors," Computational Statistics, Springer, vol. 32(1), pages 71-91, March.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:1:d:10.1007_s00180-016-0699-6
    DOI: 10.1007/s00180-016-0699-6
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    References listed on IDEAS

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    1. M. J. Bayarri & G. García‐Donato, 2008. "Generalization of Jeffreys divergence‐based priors for Bayesian hypothesis testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 981-1003, November.
    2. Chang, Ching-Hui & Pal, Nabendu, 2008. "Testing on the common mean of several normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 321-333, December.
    3. K. Krishnamoorthy & Yong Lu, 2003. "Inferences on the Common Mean of Several Normal Populations Based on the Generalized Variable Method," Biometrics, The International Biometric Society, vol. 59(2), pages 237-247, June.
    4. Fulvio De Santis & Fulvio Spezzaferri, 1999. "Methods for Default and Robust Bayesian Model Comparison: the Fractional Bayes Factor Approach," International Statistical Review, International Statistical Institute, vol. 67(3), pages 267-286, December.
    5. William R. Fairweather, 1972. "A Method of Obtaining an Exact Confidence Interval for the Common Mean of Several Normal Populations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(3), pages 229-233, November.
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