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The empirical Bayes estimators of the mean and variance parameters of the normal distribution with a conjugate normal-inverse-gamma prior by the moment method and the MLE method

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  • Ying-Ying Zhang
  • Teng-Zhong Rong
  • Man-Man Li

Abstract

Most of the samples in the real world are from the normal distributions with unknown mean and variance, for which it is common to assume a conjugate normal-inverse-gamma prior. We calculate the empirical Bayes estimators of the mean and variance parameters of the normal distribution with a conjugate normal-inverse-gamma prior by the moment method and the Maximum Likelihood Estimation (MLE) method in two theorems. After that, we illustrate the two theorems for the monthly simple returns of the Shanghai Stock Exchange Composite Index.

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  • Ying-Ying Zhang & Teng-Zhong Rong & Man-Man Li, 2019. "The empirical Bayes estimators of the mean and variance parameters of the normal distribution with a conjugate normal-inverse-gamma prior by the moment method and the MLE method," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(9), pages 2286-2304, May.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:9:p:2286-2304
    DOI: 10.1080/03610926.2018.1465081
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    Cited by:

    1. Li Zhang & Ying-Ying Zhang, 2022. "The Bayesian Posterior and Marginal Densities of the Hierarchical Gamma–Gamma, Gamma–Inverse Gamma, Inverse Gamma–Gamma, and Inverse Gamma–Inverse Gamma Models with Conjugate Priors," Mathematics, MDPI, vol. 10(21), pages 1-27, October.

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