• 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.

• 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.

• 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.

• 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.33 no.2
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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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• v.24 no.4
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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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• v.8 no.2
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• pp.183-194
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• 1997

In accelerated life tests, the failure time of an item is observed under a high stress level and based on the time, the failure rates of items we estimated at the normal stress level. In this paper, when the mean of the prior distribution of a parameter is known in Weibull lifetime model with censored failure time data, we study various estimating methods to obtain the empirical Bayes estimator of a parameter from the empirical Bayes approach under the normal stress level by considering the fact that the Bayes estimator is the function of prior parameters and of the acceleration parameter representing the effect of acceleration. And we compare the performance of several empirical Bayes estimators of a parameter in terms of the Bayes risk.

• Journal of the Korean Statistical Society
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• v.20 no.2
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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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• v.15 no.2
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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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• v.8 no.2
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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.