• 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.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.55-79
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• 2015

It is well known that using any additional information in the estimation of unknown parameters with new sample of observations diminishes the sampling units needed and minimizes the risk of new estimators. There are many rational reasons to assure that the existence of additional information in practice and there exists many practical cases in which additional information is available in the form of target value (initial value) about the unknown parameters. This article is described the problem of how the prior initial value about the unknown parameters can be utilized and combined with classical Bayes estimator to get a new combination of Bayes estimator and prior value to improve the properties of the new combination. In this article, two classes of Bayes-shrinkage and preliminary test Bayes-shrinkage estimators are proposed for the scale parameter of exponential distribution. The bias, risk and risk ratio expressions are derived and studied. The performance of the proposed classes of estimators is studied for different choices of constants engaged in the estimators. The comparisons, conclusions and recommendations are demonstrated.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.95-110
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• 1996

We consider the question of efficiency of the Bayes sequential procedure with respect to the optimal fixed sample size Bayes procedure in a simple vs. simple testing problem for data coming from a general nonregular density b(.theta.)h(x)l(x < .theta.). Efficiency is defined in two different ways in these caiculations. Also, the minimax sequential risk (and minimax sequential stratage) is studied as a function of the cost of sampling.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.1-10
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• 2002

A Bayes estimator of the scale parameter in an exponential distribution will be considered by a LINEX error, then the risk of the Bayes estimator using a LINEX loss will be compared with that of a Bayes estimator using a square error.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.487-500
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• 1999

We propose a class of hierarchical Bayes estimators of the error variance under the relative squared error loss in balanced fixed-effects two-way analysis of variance models. Also we provide analytic expressions for the risk improvement of the hierarchical Bayes estimators over multiples of the error sum of squares. Using these expressions we identify a subclass of the hierarchical Bayes estimators each member of which dominates the best multiple of the error sum of squares which is known to be minimax. Numerical values of the percentage risk improvement are given in some special cases.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.261-274
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• 2014

In this paper we develop Bayes and empirical Bayes estimators of the finite population mean with the assumption of posterior linearity rather than normality of the superpopulation under the balanced loss function. We compare the performance of the optimal Bayes estimator with ones of the classical sample mean and the usual Bayes estimator under the squared error loss with respect to the posterior expected losses, risks and Bayes risks when the underlying distribution is normal as well as when they are binomial and Poisson.

• Proceedings of the IEEK Conference
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• 2001.06d
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• pp.159-162
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• 2001

In this Paper, a new multi-sensor single-target tracking method in cluttered environment is proposed. Unlike the established methods such as probabilistic data association filter (PDAF), the proposed method intends to reflect the information in detection phase into parameters in tracking so as to reduce uncertainty due to clutter. This is achieved by first modifying the Bayes risk in Bayesian detection criterion to incorporate the likelihood of measurements from multiple sensors. The final estimate is then computed by taking a linear combination of the likelihood and the estimate of measurements. We develop the procedure and discuss the results from representative simulations.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.235-243
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• 2014

Constrained Bayesian estimates overcome the over shrinkness toward the mean which usual Bayes and empirical Bayes estimates produce by matching first and second empirical moments; subsequently, a constrained Bayes estimate is recommended to use in case the research objective is to produce a histogram of the estimates considering the location and dispersion. The well-known squared error loss function exclusively emphasizes the precision of estimation and may lead to biased estimators. Thus, the balanced loss function is suggested to reflect both goodness of fit and precision of estimation. In insurance pricing, the accurate location estimates of risk and also dispersion estimates of each risk group should be considered under proper loss function. In this paper, by applying these two ideas, the benefit of the constrained Bayes estimates and balanced loss function will be discussed; in addition, application effectiveness will be proved through an analysis of real insurance accident data.

• 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.

• Journal of Korean Society for Quality Management
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• v.13 no.1
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• pp.2-11
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• 1985

We study some Bayes esimators of the reliability of k out of m stress-strength model under quadratic loss and various prior distributions. We obtain Bayes estimators, Bayes risk, predictive bounds and asymtotic distribution of Bayes estimator. We investigate behaviours of Bayes estimator in moderate samples.