• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.443-461
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• 2009

In order to overcome the lack of Korean credit rating migration data, we consider an empirical Bayes procedure to estimate credit rating migration matrices. We derive the posterior probabilities of Korean credit rating transitions by utilizing the Moody's rating migration data and the credit rating assignments from Korean rating agency as prior information and likelihood, respectively. Metrics based upon the average transition probability are developed to characterize the migration matrices and compare our Bayesian migration matrices with some given matrices. Time series data for the metrics show that our Bayesian matrices are stable, while the matrices based on Korean data have large variation in time. The bootstrap tests demonstrate that the results from the three estimation methods are significantly different and the Bayesian matrices are more affected by Korean data than the Moody's data. Finally, Monte Carlo simulations for computing the values of a portfolio and its credit VaRs are performed to compare these migration matrices.

• Journal of applied mathematics & informatics
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• v.3 no.1
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• pp.55-64
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• 1996

Let $X_1, ....$X_P be p($\geq$2) independent random variables, where each X1 has a gamma distribution with $k_i and ${\heta}_i$. The problem is to simultaneously estimate p gammar parameters ${\heta}_i$ under entropy loss where the parameters are believed priori. Hierarchical bayes(HB) and empirical bayes(EB) estimators are investigated. Next computer simulation is studied to compute the risk percentage improvement of the HB, EB and the estimator of Dey et al.(1987) compared to MVUE of ${\heta}$.

• Interdisciplinary Bio Central
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• v.2 no.2
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• pp.4.1-4.6
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• 2010

The most common type of microarray experiment has a simple design using microarray data obtained from two different groups or conditions. A typical method to identify differentially expressed genes (DEGs) between two conditions is the conventional Student's t-test. The t-test is based on the simple estimation of the population variance for a gene using the sample variance of its expression levels. Although empirical Bayes approach improves on the t-statistic by not giving a high rank to genes only because they have a small sample variance, the basic assumption for this is same as the ordinary t-test which is the equality of variances across experimental groups. The t-test and empirical Bayes approach suffer from low statistical power because of the assumption of normal and unimodal distributions for the microarray data analysis. We propose a method to address these problems that is robust to outliers or skewed data, while maintaining the advantages of the classical t-test or modified t-statistics. The resulting data transformation to fit the normality assumption increases the statistical power for identifying DEGs using these statistics.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.261-276
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• 1997

In the context of binary response regression, the problem of constructing Bayesian goodness-of-link test for testing logit link versus probit link is considered. Based upon the well known facts that cdf of logistic variate .approx. cdf of $t_{8}$/.634 and, as .nu. .to. .infty., cdf of $t_{\nu}$ approximates to that of N(0,1), Bayes factor is derived as a test criterion. A synthesis of the Gibbs sampling and a marginal likelihood estimation scheme is also proposed to compute the Bayes factor. Performance of the test is investigated via Monte Carlo study. The new test is also illustrated with an empirical data example.e.

• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.121-150
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• 2003

The National Health Interview Survey (NHIS) is one of the surveys used to assess the health status of the US population. One indicator of the nation's health is the total number of doctor visits made by the household members in the past year, There is a substantial nonresponse among the sampled households, and the main issue we address here is that the nonrespones mechanism should not be ignored because respondents and nonrespondents differ. It is standard practice to summarize the number of doctor visits by the binary variable of no doctor visit versus at least one doctor visit by a household for each of the fifty states and the District of Columbia. We consider a nonignorable nonresponse model that expresses uncertainty about ignorability through the ratio of odds of a household doctor visit among respondents to the odds of doctor visit among all households. This is a hierarchical model in which a nonignorable nonresponse model is centered on an ignorable nonresponse model. Another feature of this model is that it permits us to "borrow strength" across states as in small area estimation; this helps because some of the parameters are weakly identified. However, for simplicity we assume that the hyperparameters are fixed but unknown, and these hyperparameters are estimated by the EM algorithm; thereby making our method Bayes empirical Bayes. Our main result is that for some of the states the nonresponse mechanism can be considered non-ignorable, and that 95% credible intervals of the probability of a household doctor visit and the probability that a household responds shed important light on the NHIS.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.159-172
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• 1994

An empirical Bayes estimator of the probability of discovering a new species is proposed when some prior information is available on the number f species. The new estimator is shown via simulations to have only a moderate bias and a smaller RMSE than Good's estimator when the species population follows a truncated geometric distribution.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.5D
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• pp.453-459
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• 2010

In the study of traffic safety, it is utmost important to obtain more reliable estimates of the expected crashes for a site (or a segment). The observed crashes have been mainly used as the estimate of the expected crashes in Korea, while the empirical Bayes (EB) estimates based on the Poisson-gamma mixture model have been used in the USA and several European countries. Although numerous studies have used the EB method for estimating the expected crashes and/or the effectiveness of the safety countermeasures, no past studies examine the difference in the estimation errors between the two estimates. Thus, this study compares the estimation errors of the two estimates using a Monte Carlo simulation study. By analyzing the crash dataset at 3,000,000 simulated sites, this study reveals that the estimation errors of the EB estimates are always less than those of the observed crashes. Hence, it is imperative to incorporate the EB method into the traffic safety research guideline in Korea. However, the results show that the differences in the estimation errors between the two estimates decrease as the uncertainty of the prior distribution increases. Consequently, it is recommended that the EB method be used with reliable hyper-parameter estimates after conducting a comprehensive examination on the estimated negative binomial model.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.1-5
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• 2002

We consider the problem of optimal bandwidth choice for nonparametric classification, based on kernel density estimators, where the problem of interest is distinguishing between two univariate distributions. When the densities intersect at a single point, optimal bandwidth choice depends on curvatures of the densities at that point. The problem of empirical bandwidth selection and classifying data in the tails of a distribution are also addressed.

• The Mathematical Education
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• v.23 no.1
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• pp.45-50
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• 1984

A problem of estimating the means of Poisson populations using independent samples is considered. The total loss is the sum of component, normalized squared error losses. An empirical Bayes estimator is derived and compared, by Monte Carlo methods, with existing estimators which are proposed as improving estimators upon the usual one. Monte Carlo results show that the performance of the derived estimator is satisfactory over the whole parameter space.

• Asian-Australasian Journal of Animal Sciences
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• v.14 no.11
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• pp.1511-1515
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• 2001

A prediction of 305 d milk production from early records using an empirical Bayes method (EBM) was performed. The EBM was compared with the best predicted estimation (BPE), test interval method (TIM), and the linearized Wood's model (LWM). Daily milk yields were obtained from 606 first lactation Japanese Holstein cows in three herds. From each file of 305 daily records, 10 random test day records with an interval of approximately one month were taken. The accuracies of these methods were compared using the absolute difference (AD) and the standard deviation (SD) of the differences between the actual and the estimated 305 d milk production. The results showed that in the early stage of the lactation, EBM was superior in obtaining the prediction with high accuracy. When all the herds were analyzed jointly, the AD during the first 5 test day records were on average 373, 590, 917 and 1,042 kg for EBM, BPE, TIM, and LWM, respectively. Corresponding SD for EBM, BPE, TIM, and LWM were on average 488, 733, 747 and 1,605 kg. When the herds were analyzed separately, the EBM predictions retained high accuracy. When more information on the actual lactation was added to the prediction, TIM and LWM gradually achieved better accuracies. Finally, in the last period of the lactation, the accuracy of both of the methods exceeded EBM and BPM. The AD for the last 2 samples analyzing all the herds jointly were on average 141, 142, 164, and 214 kg for LWM, TIM, EBM, and BPE, respectively. In the current practices of collecting monthly records, early prediction of future milk production may be more accurate using EBM. Alternatively, if enough information of the actual lactation is accumulated, TIM may obtain better accuracy in the latter stage of lactation.