• 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.

• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.173-181
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• 1993

Nonparametric empirical Bayes estimation of a distribution function with respect to dirichlet process prior is considered when sample sizes are varying from component to component. Zehnwirth's estimate of $\alpha$(R) is modified to be used in our empirical Bayes problem with non-identical components.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.145-154
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• 1995

Empirical Bayes approach is applied to estimation of the binomial parameter when there is a cost for observations. Both the sample size and the decision rule for estimating the parameter are determined stochastically by the data, making the result more useful in applications. Our empirical Bayes problems with non-iid components are compared to the usual empirical Bayes problems with iid components. The asymptotic optimal procedure with a computer simulation is given.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.235-243
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• 2014

Constrained Bayesian estimates overcome the over shrinkness toward the mean which usual Bayes and empirical Bayes estimates produce by matching first and second empirical moments; subsequently, a constrained Bayes estimate is recommended to use in case the research objective is to produce a histogram of the estimates considering the location and dispersion. The well-known squared error loss function exclusively emphasizes the precision of estimation and may lead to biased estimators. Thus, the balanced loss function is suggested to reflect both goodness of fit and precision of estimation. In insurance pricing, the accurate location estimates of risk and also dispersion estimates of each risk group should be considered under proper loss function. In this paper, by applying these two ideas, the benefit of the constrained Bayes estimates and balanced loss function will be discussed; in addition, application effectiveness will be proved through an analysis of real insurance accident data.

• Communications for Statistical Applications and Methods
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• v.20 no.4
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• pp.321-327
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• 2013

Bayesian and empirical Bayesian methods have become quite popular in the theory and practice of statistics. However, the objective is to often produce an ensemble of parameter estimates as well as to produce the histogram of the estimates. For example, in insurance pricing, the accurate point estimates of risk for each group is necessary and also proper dispersion estimation should be considered. Well-known Bayes estimates (which is the posterior means under quadratic loss) are underdispersed as an estimate of the histogram of parameters. The adjustment of Bayes estimates to correct this problem is known as constrained Bayes estimators, which are matching the first two empirical moments. In this paper, we propose a way to apply the constrained Bayes estimators in insurance pricing, which is required to estimate accurately both location and dispersion. Also, the benefit of the constrained Bayes estimates will be discussed by analyzing real insurance accident data.

• 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.

• 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.

• Journal of Korean Society for Quality Management
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• v.19 no.2
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• pp.86-95
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• 1991

Empirical Bayes estimation of the binomial parameter ${\theta}$ is considered when the sample size in each component problem is random. The result is applied to the lot acceptance sampling problem in the presence of various kinds of costs including cost for sampling.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.845-852
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• 2010

The outcomes of counts commonly occur in the area of disease mapping for mortality rates or disease rates. A Poisson distribution is usually assumed as a model of disease rates in conjunction with a gamma prior. The small area typically refers to a small geographical area or demographic group for which very little information is available from the sample surveys. Under this situation the model-based estimation is very popular, in which the auxiliary variables from various administrative sources are used. The empirical Bayes estimator under Poissongamma model has been considered with its accuracy measures. An accuracy measure using a bootstrap samples adjust the underestimation incurred by the posterior variance as an estimator of true mean squared error. We explain the suggested method through a practical dataset of hitters in baseball games. We also perform a Monte Carlo study to compare the accuracy measures of mean squared error.

• Journal of Korean Society for Quality Management
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• v.43 no.1
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• pp.57-66
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• 2015

Purpose: The purpose of this study is to apply the constrained Bayesian estimation methodology for product quality control process and prove the effectiveness of the product management by comparing with the well-known Bayes estimator through data performance result. Methods: The Bayes and constrained Bayes estimators were produced based on the theoretical background and for confirming the effectiveness of suggested application, the deviation index was defined and calculated for the comparison. Results: The statistical analysis result shows that applying the suggested estimation methodology, that is, constrained Bayes estimator improves the effectiveness of the index with regard to reduce the error by matching the first two empirical moments. Conclusion: Considering the advanced Bayesian approaches such as constrained Bayes estimation for the product quality control process, the newly defined deviation index reduces the error for estimating the parameter histogram which is reflected both location and deviation parameters and furthermore various Bayesian perspective approaches seems to be meaningful for managing the product quality control process.