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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| Authors: | Ying-Ying Zhang Teng-Zhong Rong Man-Man Li |
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| Institution: | Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, China |
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| 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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| Keywords: | Empirical bayes estimators moment method maximum likelihood estimation (MLE) method normal distribution with normal-inverse-gamma prior non standardized student-t distribution |
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