Estimation of Geometric Mean for k Exponential Parameters Using a Probability Matching Prior

Title & Authors
Estimation of Geometric Mean for k Exponential Parameters Using a Probability Matching Prior
Kim, Hea-Jung; Kim, Dae Hwang;

Abstract
In this article, we consider a Bayesian estimation method for the geometric mean of $\small{textsc{k}}$ exponential parameters, Using the Tibshirani's orthogonal parameterization, we suggest an invariant prior distribution of the $\small{textsc{k}}$ parameters. It is seen that the prior, probability matching prior, is better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile. Then a weighted Monte Carlo method is developed to approximate the posterior distribution of the mean. The method is easily implemented and provides posterior mean and HPD(Highest Posterior Density) interval for the geometric mean. A simulation study is given to illustrates the efficiency of the method.
Keywords
Bayesian estimation;geometric mean;invariant prior;weighted Monte Carlo method;
Language
Korean
Cited by
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