• Communications for Statistical Applications and Methods
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• 제2권1호
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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.

• International Journal of Reliability and Applications
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• 제2권1호
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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.

• 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.

• 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.

• Journal of the Korean Statistical Society
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• 제33권2호
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• pp.191-202
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• 2004

The paper considers nonparametric empirical Bayes estimation of residual survival function at age t using a Dirichlet process prior V(a). Empirical Bayes estimators are proposed for the case where both the function ${\alpha}$(0, $\chi$] and the size a(R$\^$+/) are unknown. It is shown that the proposed empirical Bayes estimators are asymptotically optimal at a rate n$\^$-1/, where n is the number of past data available for the present estimation problem. Therefore, the result of Lahiri and Park (1988) in which a(R$\^$+/) is assumed to be known and a rate n$\^$-1/ is achieved, is extended to a(R$\^$+/) unknown case.

• Journal of the Korean Data and Information Science Society
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• 제24권4호
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• pp.885-893
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• 2013

This paper considers Bayes estimations of the small area means under Fay-Herriot model with measurement errors. We provide empirical Bayes predictors of small area means with the corresponding jackknifed mean squared prediction errors. Also we obtain hierarchical Bayes predictors and the corresponding posterior standard deviations using Gibbs sampling. Numerical studies are provided to illustrate our methods and compare their eciencies.

• Journal of the Korean Data and Information Science Society
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• 제8권2호
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• pp.183-194
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• 1997

이 논문의 목적은 제2종 중도절단자료된 가속수명 자료가 형상모수를 고정시킨 와이블분포를 한다는 가정에서 데이터에 대한 경험적베이즈 방법을 이용하여 분석하는데 있다. 이 논문에서는 적률추정법과 최우추정법을 이용한 경험적 베이지안 방법을 제안하고, Pathak등에 의해 제안된 경험적베이지안 방법과 비교한다. 특히, 인위적 자료를 이용한 모의 실험을 통하여 추정량들을 추정된 베이즈위험측면에서 비교한다.

• Journal of the Korean Statistical Society
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• 제20권2호
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• pp.108-117
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• 1991

A parametric empirical Bayes procedure is proposed and studied to compare treatments simultaneously with the best. Minimum Bayes risk lower bounds are derived for an additive loss function, and their relationship with Bayesian simultaneous confidence lower bounds is given. For the proposed empirical Bayes procedure, the nominal confidence level both in Bayesian sense and in frequentist's sense is shown to be controlled asymptotically. For practical implementation, a measure of significance similar to f-value is suggested with an illustrative example.

• Communications for Statistical Applications and Methods
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• 제15권2호
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• pp.213-228
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• 2008

Using a linear loss function, this paper considers the one-sided testing problem for the exponential distribution via the empirical Bayes(EB) approach. Based on right censored data, we propose an EB test for the exponential parameter and obtain its convergence rate and asymptotic optimality, firstly, under the condition that the censoring distribution is known and secondly, that it is unknown.

• Journal of the Korean Data and Information Science Society
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• 제8권2호
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• pp.261-270
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• 1997

This paper is proposed the parametric empirical Bayes(EB) confidence intervals which corrects the deficiencies in the naive EB confidence intervals of the scale parameter in the Weibull distribution under item-censoring scheme. In this case, the bootstrap EB confidence intervals are obtained by the parametric bootstrap introduced by Laird and Louis(1987). The comparisons among the bootstrap and the naive EB confidence intervals through Monte Carlo study are also presented.