• Communications for Statistical Applications and Methods
• /
• v.14 no.1
• /
• pp.71-80
• /
• 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.

• Journal of the Korean Statistical Society
• /
• v.24 no.1
• /
• pp.161-181
• /
• 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.

• The Korean Journal of Applied Statistics
• /
• v.27 no.6
• /
• pp.1017-1028
• /
• 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 applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.147-149
• /
• 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
• /
• v.30 no.3
• /
• pp.481-498
• /
• 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.

• International Journal of Reliability and Applications
• /
• v.2 no.1
• /
• pp.49-56
• /
• 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 the Korean Data and Information Science Society
• /
• v.10 no.1
• /
• pp.155-162
• /
• 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.

• Journal of the Korean Statistical Society
• /
• v.33 no.2
• /
• pp.191-202
• /
• 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
• /
• v.17 no.3
• /
• pp.1009-1019
• /
• 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 applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.305-317
• /
• 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 $O(n^{-q}),\;q\;=\;{\lambda}s(\delta\;-\;2)/\delta(s\;+\;2)$.