• Journal of the Korean Statistical Society
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• 제27권1호
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• pp.11-23
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• 1998

A Bayes criterion for testing the equality of covariance matrices of two multivariate normal distributions is proposed and studied. Development of the criterion invloves calculation of Bayes factor using the imaginary sample method introduced by Spiegelhalter and Smith (1982). The criterion is designed to develop a Bayesian test criterion, so that it provides an alternative test criterion to those based upon asymptotic sampling theory (such as Box's M test criterion). For the constructed criterion, numerical studies demonstrate routine application and give comparisons with the traditional test criteria.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.97-107
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• 2001

A simultaneous test criterion for multiple hypotheses concerning comparison of two multivariate normal populations is considered by using the so called Bayes factor method. Fully parametric frequentist approach for the test is not available and thus Bayesian criterion is pursued using a Bayes factor that eliminates its arbitrariness problem induced by improper priors. Specifically, the fractional Bayes factor (FBF) by O'Hagan (1995) is used to derive the criterion. Necessary theories involved in the derivation an computation of the criterion are provided. Finally, an illustrative simulation study is given to show the properties of the criterion.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.55-64
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• 2000

We propose a criterion for testing homogeneity of matrix intraclass covariance matrices of K multivariate normal populations, It is based on a variable transformation intended to propose and develop a likelihood ratio criterion that makes use of properties of eigen structures of the matrix intraclass covariance matrices. The criterion then leads to a simple test that uses an asymptotic distribution obtained from Box's (1949) theorem for the general asymptotic expansion of random variables.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.473-481
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• 2005

The testing problem for sphericity structure of the covariance matrix in a multivariate normal distribution is introduced when there is a sample with 2-step monotone missing data pattern. The maximum likelihood method is described to estimate the parameters on the basis of the sample. Using these estimates, the likelihood ratio criterion for testing sphericity is derived.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.929-938
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• 1999

We propose a criterion for testing homogeneity of diagonal covariance matrices of K multivariate normal populations. It is based on a factorization of usual likelihood ratio intended to propose and develop a criterion that makes use of properties of structures of the diagonal convariance matrices. The criterion then leads to a simple test as well as to an accurate asymptotic distribution of the test statistic via general result by Box (1949).

• 대한수학회보
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• 제38권2호
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• pp.379-387
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• 2001

In this paper, we study the value distribution of meromorphic functions and prove the following theorem: Let f(z) be a transcendental meromorphic function. If f and f'have the same zeros, then f'(z) takes any non-zero value b infinitely many times.

• Communications for Statistical Applications and Methods
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• 제26권3호
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• pp.273-293
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• 2019

We consider the problem of model selection in multiple linear regression with outliers and non-normal error distributions. In this article, the robust model selection criterion is proposed based on the robust estimation method with the least absolute deviation (LAD). The proposed criterion is shown to be consistent. We suggest proposed criterion based algorithms that are suitable for a large number of predictors in the model. These algorithms select only relevant predictor variables with probability one for large sample sizes. An exhaustive simulation study shows that the criterion performs well. However, the proposed criterion is applied to a real data set to examine its applicability. The simulation results show the proficiency of algorithms in the presence of outliers, non-normal distribution, and multicollinearity.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.193-205
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• 1999

An approximate Bayes criterion for Behrens-Fisher problem (testing equality of means of two normal populations with unequal variances) is proposed and examined. Development of the criterion involves derivation of approximate Bayes factor using the imaginary training sample approachintroduced by Spiegelhalter and Smith (1982). The proposed criterion is designed to develop a Bayesian test criterion having a closed form, so that it provides an alternative test to those based upon asymptotic sampling theory (such as Welch's t test). For the suggested Bayes criterion, numerical study gives comparisons with a couple of asymptotic classical test criteria.

• Korea-Australia Rheology Journal
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• 제20권1호
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• pp.15-26
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• 2008

It has been known that there is a viscoelastic instability in the channel flow past a cylinder at high Deborah (De) number. Some of our numerical simulations and a boundary layer analysis indicated that this instability is related to the shear flow in the gap between the cylinder and the channel walls in our previous work. The critical condition for instability initiation may be related to an inflection velocity profile generated by the normal stress near the cylinder surface. At high De, the elastic normal stress coupling with the streamline curvature is responsible for the shear instability, which has been recognized by the community. In this study, an instability criterion for the flow problem is proposed based on the analysis on the pressure gradient and some supporting numerical simulations. The critical De number for various model fluids is given. It increases with the geometrical aspect ratio h/R (half channel width/cylinder radius) and depends on a viscosity ratio ${\beta}$(polymer viscosity/total viscosity) of the model. A shear thinning first normal stress coefficient will delay the instability. An excellent agreement between the predicted critical Deborah number and reported experiments is obtained.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.11-21
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• 2007

In this paper, we consider a decision-theoretic oriented, objective Bayesian inference for the difference between two normal means with unknown com-mon variance. We derive the Bayesian reference criterion as well as the intrinsic estimator and the credible region which correspond to the intrinsic discrepancy loss and the reference prior. We illustrate our results using real data analysis as well as simulation study.