• Communications for Statistical Applications and Methods
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• v.14 no.1
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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.

• 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.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.305-317
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• 2004

We construct the empirical Bayes (EB)estimation of the parameter in two-side truncated distribution families with asymmetric Linex loss using negatively associated (NA) samples. The asymptotical optimality and convergence rate of the EB estimation is obtained. We will show that the convergence rate can be arbitrarily close to $O(n^{-q}),\;q\;=\;{\lambda}s(\delta\;-\;2)/\delta(s\;+\;2)$.

• 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 applied mathematics & informatics
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• v.19 no.1_2
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• pp.147-149
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• 2005

Recently, there are some empirical Bayes procedures using NA samples. We point out a key equality which may not hold for NA samples. Thus, the results of those empirical Bayes procedures based on NA samples are dubious

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.481-498
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• 2001

Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.87-96
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• 2001

We consider the empirical Bayes estimation problems with the binomial and normal components when the prior distributions are unknown but are assumed to be in certain families. There may be the families of all distributions on the parameter space or subfamilies such as the parametric families of conjugate priors. We treat both cases and establish the asymptotic optimality for the corresponding decision procedures.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.1009-1019
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• 2006

In this paper, we consider the simultaneous estimation problem for the normal means. We set up the model structure using the several different distributions of the errors for observing their effects of model perturbation for the error terms in obtaining the empirical Bayes and hierarchical Bayes estimators. We compare the performance of those estimators under model perturbation based on a simulation study.

• Journal of the Korean Statistical Society
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• v.24 no.1
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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.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.155-162
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• 1999

This paper is concerned with the empirical Bayes estimation of one of the two shape parameters(${\theta}$) in the Burr(${\beta},\;{\theta}$) type XII failure model based on type-II censored data. We obtain the bootstrap empirical Bayes confidence intervals of ${\theta}$ by the parametric bootstrap introduced by Laird and Louis(1987). The comparisons among the bootstrap and the naive empirical Bayes confidence intervals through Monte Carlo study are also presented.