• Journal of the Korean Data and Information Science Society
• /
• v.17 no.2
• /
• pp.291-300
• /
• 2006

In this research, the performance of widely used Bayesian estimators such as Bayes estimator, empirical Bayes estimator, constrained Bayes estimator and constrained empirical Bayes estimator are compared by means of a measurement under balanced loss function for the typical normal-normal situation. The proposed measurement is a weighted sum of the precisions of first and second moments. As a result, one can gets the criterion according to the size of prior variance against the population variance.

• Journal of the Korean Data and Information Science Society
• /
• v.16 no.2
• /
• pp.371-382
• /
• 2005

The paper compares the performance of some widely used Bayesian estimators such as Bayes estimator, empirical Bayes estimator, constrained Bayes estimator and constrained Bayes estimator by means of a new measurement under squared error loss function for the typical normal-normal situation. The proposed measurement is a weighted sum of the precisions of first and second moments. As a result, one can gets the criterion according to the size of prior variance against the population variance.

• Journal of the Korean Data and Information Science Society
• /
• v.15 no.1
• /
• pp.273-284
• /
• 2004

Bayes estimation of parameters is considered for two independent exponential distributions with ordered means. Order restricted Bayes estimators for means are obtained with respect to inverted gamma, noninformative prior and uniform prior distributions, and their asymptotic properties are established. It is shown that the maximum likelihood estimator, restricted maximum likelihood estimator, unrestricted Bayes estimator, and restricted Bayes estimator of the mean are all consistent and have the same limiting distribution. These estimators are compared with the corresponding unrestricted Bayes estimators by Monte Carlo simulation.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.12 no.2
• /
• pp.97-108
• /
• 2008

In this paper Bayes estimator of the parameter and reliability function of the zero-truncated Poisson distribution are obtained. Furthermore, recurrence relations for the estimator of the parameter are also derived. Monte Carlo simulation technique has been made for comparing the Bayes estimator and reliability function with the corresponding maximum likelihood estimator (MLE) of zero-truncated Poisson distribution.

• Communications for Statistical Applications and Methods
• /
• v.28 no.4
• /
• pp.315-327
• /
• 2021

The Spatial Autoregressive (SAR) models have drawn considerable attention in recent econometrics literature because of their capability to model the spatial spill overs in a feasible way. While considering the Bayesian analysis of these models, one may face the problem of lack of robustness with respect to underlying prior assumptions. The generalized Bayes estimators provide a viable alternative to incorporate prior belief and are more robust with respect to underlying prior assumptions. The present paper considers the SAR model with a set of linear restrictions binding the regression coefficients and derives restricted generalized Bayes estimator for the coefficients vector. The minimaxity of the restricted generalized Bayes estimator has been established. Using a simulation study, it has been demonstrated that the estimator dominates the restricted least squares as well as restricted Stein rule estimators.

• 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 the Korean Statistical Society
• /
• v.27 no.3
• /
• pp.331-348
• /
• 1998

In this paper, we have proposed some robust Bayes estimators using ML-II priors as well as certain empirical Bayes estimators in estimating the finite population mean in the presence of auxiliary information. These estimators are compared with the classical ratio estimator and a subjective Bayes estimator utilizing the auxiliary information in terms of "posterior robustness" and "procedure robustness" Also, we have addressed the issue of choice of sampling design from a robust Bayesian viewpoint.

• The Journal of Asian Finance, Economics and Business
• /
• v.5 no.3
• /
• pp.19-29
• /
• 2018

This research examined the alternatives of Jensen's alpha (α) estimation models in the Capital Asset Pricing Model, discussed by Treynor (1961), Sharpe (1964), and Lintner (1965), using the robust maximum likelihood type m-estimator (MM estimator) and Bayes estimator with conjugate prior. According to finance literature and practices, alpha has often been estimated using ordinary least square (OLS) regression method and monthly return data set. A sample of 50 securities is randomly selected from the list of the S&P 500 index. Their daily and monthly returns were collected over a period of the last five years. This research showed that the robust MM estimator performed well better than the OLS and Bayes estimators in terms of efficiency. The Bayes estimator did not perform better than the OLS estimator as expected. Interestingly, we also found that daily return data set would give more accurate alpha estimation than monthly return data set in all three MM, OLS, and Bayes estimators. We also proposed an alternative market efficiency test with the hypothesis testing Ho: α = 0 and was able to prove the S&P 500 index is efficient, but not perfect. More important, those findings above are checked with and validated by Jackknife resampling results.

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

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