• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.291-300
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• 2006

In this research, the performance of widely used Bayesian estimators such as Bayes estimator, empirical Bayes estimator, constrained Bayes estimator and constrained empirical Bayes estimator are compared by means of a measurement under balanced loss function for the typical normal-normal situation. The proposed measurement is a weighted sum of the precisions of first and second moments. As a result, one can gets the criterion according to the size of prior variance against the population variance.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.371-382
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• 2005

The paper compares the performance of some widely used Bayesian estimators such as Bayes estimator, empirical Bayes estimator, constrained Bayes estimator and constrained Bayes estimator by means of a new measurement under squared error loss function for the typical normal-normal situation. The proposed measurement is a weighted sum of the precisions of first and second moments. As a result, one can gets the criterion according to the size of prior variance against the population variance.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.331-348
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• 1998

In this paper, we have proposed some robust Bayes estimators using ML-II priors as well as certain empirical Bayes estimators in estimating the finite population mean in the presence of auxiliary information. These estimators are compared with the classical ratio estimator and a subjective Bayes estimator utilizing the auxiliary information in terms of "posterior robustness" and "procedure robustness" Also, we have addressed the issue of choice of sampling design from a robust Bayesian viewpoint.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1017-1028
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• 2014

Well-known Bayes and empirical Bayes estimators have a disadvantage in respecting to overshink the parameter estimator error; therefore, a constrained Bayes estimator is suggested by matching the first two moments. Also traditional loss function such as mean square error loss function only considers the precision of estimation and to consider both precision and goodness of fit, balanced loss function is suggested. With these reasons, constrained Bayes estimators under balanced loss function is recommended for non-life insurance pricing.; however, most studies focus on the performance of estimation since Bayes risk of newly suggested estimators such as constrained Bayes and constrained empirical Bayes estimators under specific loss function is difficult to derive. This study compares the Bayes risk of several Bayes estimators under two different loss functions for estimating the risk in the auto insurance business and indicates the effectiveness of the newly suggested Bayes estimators with regards to Bayes risk perspective through auto insurance real data analysis.

• Journal of the Korean Statistical Society
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• v.15 no.2
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• pp.97-106
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• 1986

Assume that $X_1, X_2, \cdots, X_N$ are iid p-dimensional normal random vectors ($p \geq 3$) with unknown covariance matrix. The problem of estimating multivariate normal mean vector in an empirical Bayes situation is considered. Empirical Bayes estimators, obtained by Bayes treatmetn of the covariance matrix, are presented. It is shown that the estimators are minimax, each of which domainates teh maximum likelihood estimator (MLE), when the loss is nonsingular quadratic loss. We also derive approximate credibility region for the mean vector that takes advantage of the fact that the MLE is not the best estimator.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.71-80
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• 2007

The present paper investigates estimation of a scale parameter of a gamma distribution using a loss function that reflects both goodness of fit and precision of estimation. The Bayes and empirical Bayes estimators rotative to balanced loss functions (BLFs) are derived and optimality of some estimators are studied.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.221-235
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• 1999

Let be $X_1$,...,$X_p$, $p\geq2$ independent random variables where each $X_i$ has a gamma distribution with $\textit{k}_i$ and $\theta_i$ The problem is to simultaneously estimate $\textit{p}$ gamma parameters $\theta_i$ and $\theta_i{^-1}$ under entropy loss where the parameters are believed priori. Hierarch ical Bayes(HB) and empirical Bayes(EB) estimators are investigated. And a preference of HB estimator over EB estimator is shown using Gibbs sampler(Gelfand and Smith 1990). Finally computer simulation is studied to compute the risk percentage improvements of the HB estimator and the estimator of Dey Ghosh and Srinivasan(1987) compared to UMVUE estimator of $\theta^{-1}$.

• Journal of Korean Society for Quality Management
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• v.42 no.4
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• pp.747-756
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• 2014

Purpose: The purpose of this study is to apply the Bayesian estimation methodology for producing 'Korean Standard -Quality Excellence Index' model and prove the effectiveness of the new approach based on survey data by comparing the current index with the new index produced by Bayesian estimation method. Methods: The 'Korean Standard -Quality Excellence Index' was produced through the collected survey data by Bayesian estimation method and comparing the deviation with two results for confirming the effectiveness of suggested application. Results: The statistical analysis result shows that suggested estimator, that is, empirical Bayes estimator improves the effectiveness of the index with regard to reduce the error under specific loss function, which is suggested for checking the goodness of fit. Conclusion: Considering the Bayesian techniques such as empirical Bayes estimator for producing the quality excellence index reduces the error for estimating the parameter of interest and furthermore various Bayesian perspective approaches seems to be meaningful for producing the corresponding index.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.261-274
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• 2014

In this paper we develop Bayes and empirical Bayes estimators of the finite population mean with the assumption of posterior linearity rather than normality of the superpopulation under the balanced loss function. We compare the performance of the optimal Bayes estimator with ones of the classical sample mean and the usual Bayes estimator under the squared error loss with respect to the posterior expected losses, risks and Bayes risks when the underlying distribution is normal as well as when they are binomial and Poisson.

• International Journal of Reliability and Applications
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• v.2 no.1
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• pp.49-56
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• 2001

In this paper we consider empirical Bayes estimation of the hazard rate and survival probabilities with right censored data under the assumption that the hazard function is constant over the period of observation and the prior distribution is gamma. We provide an estimator of the first derivative of the prior moment generating function that converges at each point to the true value in $L_2$ and use it to obtain, easy to compute, asymptotically optimal estimators under the squared error loss function.