• 품질경영학회지
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• 제43권1호
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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.

• 응용통계연구
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• 제27권6호
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• pp.1017-1028
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• 2014

잘 알려져 있는 것처럼 일반적인 베이즈 추정량(Bayes estimator)과 경험적 베이즈 추정량(empirical Bayes estimator)은 모수를 추정하는데 있어서 오차를 과다축소하는 단점을 가지고 있다. 따라서 이러한 단점을 극복하기 위하여 constrained 베이즈 추정량이 일차 적률과 이차 적률을 일치시키는 성질을 만족시키며 제안되었다. 또한 평균 제곱오차 함수와 같은 전통적인 손실함수에서는 추정의 정확성만을 고려하는 특징을 가지고 있기 때문에, 추정의 정확성과 정합성을 동시에 고려하는 균형 손실함수가 제안되었다. 이러한 이유로 인하여 균형손실 함수하에서의 제한적 베이즈 추정량의 활용이 손해 보험의 가격 산출에 제안되는 것은 타당하다. 그러나 대부분의 연구는 추정의 문제에만 집중하는 경향이 있으며. 이는 새롭게 제안되는 특정 손실함수하에서의 constrained 베이즈 추정량과 constrained empirical 베이즈 추정량의 베이즈 위험의 계산이 어렵다는 점에서 기인한다. 본 연구에서는 다양한 베이즈 추정량들에 대한 베이즈 위험을 서로 다른 두 손실함수하에서 비교하였으며, 그 대상은 자동차 보험 산업에서의 위험도 추정 분야이다. 또한 자동차 보험 산업의 실제 사고 데이터를 이용하여 새롭게 제안된 베이즈 추정량의 베이즈 위험을 비교함으로써 그 효용성을 입증하였다.

• Communications for Statistical Applications and Methods
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• 제21권3호
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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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• 제20권4호
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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 the Korean Statistical Society
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• 제24권1호
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• pp.161-181
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• 1995

The goal of this article is to study the performances of various empirical Bayes simultaneous interval estimates for all pairwise comparisons. The considered empirical Bayes interval estimaters are those based on unbiased estimate, a hierarchical Bayes estimate and a constrained hierarchical Bayes estimate. Simulation results for small sample cases are given and an illustrative example is also provided.

• 품질경영학회지
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• 제26권4호
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• pp.151-165
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• 1998

Consider the linear multivariate regression model $Y=X_1B_1＋X_2B_2＋U$, where Vec(U)~N(0, $\sum \bigotimes I_N$). This paper is concerned with Bayes infreence of the model when it is suspected that the elements of $B_2$ are constrained in the form of intervals. The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior desnities of the parameters under a generalized conjugate prior is developed. It is shown that the a, pp.oach is straightforward to specify distributionally and to implement computationally, with output readily adopted for required inference summaries. The method developed is a, pp.ied to a real problem.