• Journal of the Korean Data and Information Science Society
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• 제17권2호
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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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• 제25권3호
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• pp.685-696
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• 2014

In this paper, we develop Bayesian inference of the finite population mean with the assumption of posterior linearity rather than normality of the superpopulation in the presence of auxiliary information under the balanced loss function. We compare the performance of the optimal Bayes estimator under the balanced loss function with ones of the classical ratio estimator and the usual Bayes estimator in terms of the posterior expected losses, risks and Bayes risks.

• 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.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.

• Communications for Statistical Applications and Methods
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• 제14권1호
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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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• 제7권3호
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• pp.767-772
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• 2000

Zellner(1994) introduced the notion of a balanced loss function in the context of a general liner model to reflect both goodness of fit and precision of estimation. We study the perspective of unifying a variety of results both frequentist and Bayesian from Poisson distributions. We show that frequentist and Bayesian results for balanced loss follow from and also imply related results for quadratic loss functions reflecting only precision of estimation. Several examples are given for Poisson distribution.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.889-898
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• 2002

In decision theoretic estimation, the loss function usually emphasizes precision of estimation. However, one may have interest in goodness of fit of the overall model as well as precision of estimation. From this viewpoint, Zellner(1994) proposed the balanced loss function which takes account of both "goodness of fit" and "precision of estimation". This paper considers estimation of the parameter of a Bernoulli distribution using Zellner's(1994) balanced loss function. It is shown that the sample mean $\overline{X}$, is admissible. More general results, concerning the admissibility of estimators of the form $a\overline{X}+b$ are also presented. Finally, minimax estimators and some numerical results are given at the end of paper,at the end of paper.