• 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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• 제5권1호
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• pp.265-275
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• 1998

In testing the partial association between two variables after controlling for the S levels of a third factor, the Mantel and Haenszel (1959) statistic is often used. Since the statistic is based on the asymptotic distribution of the sum X of S hypergeometric variates, a guideline for the minimum requirements for the application of the statistic is useful. Mantel and Fleiss (1980) developed a criterion based on the guideline for the Pearson's $X^2$ statistic. The criterion requires the distance from the expected value to the closer bound of X to be at least five. The Mantel-Fleiss (MF) criterion was studied through a simulation using the hypergeometric sampling scheme. The criterion is not satisfactory. The size of statistic exceeded nominal 0.05 level nearly 1/5 of the cases even when the criteion is met. However, the results show that the statistic is much more unstable and conservative when the criterion is not met.

• Communications for Statistical Applications and Methods
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• 제13권3호
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• pp.551-566
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• 2006

In this paper, we consider a Bayesian model selection for the intraclass correlation coefficient in familiar data. In particular, we compare two nested models such as the independence and intraclass models using the reference prior. A criterion for testing is the Bayesian Reference Criterion by Bernardo (1999) and the Intrinsic Bayes Factor by Berger and Pericchi (1996). We provide numerical examples using simulation data sets for illustration.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.29-37
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• 2001

In this paper, we consider the second order probability matching criterion for the ratio of the variance components under the one-way random effect model. It turns out that among all of the reference priors given in Ye(1994), the only one reference prior satisfies the second order matching criterion. Similar results are also obtained for the intraclass correlation as well.

• 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).

• Journal of the Korean Statistical Society
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• 제16권2호
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• pp.55-70
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• 1987

The principal components regression is one of the substitues for least squares method when there exists multicollinearity in the multiple linear regression model. It is observed graphically that the performance of the principal components regression is strongly dependent upon the values of the parameters. Accordingly, a new deletion criterion which determines proper principal components to be deleted from the analysis is developed and its usefulness is checked by simulations.

• Journal of the Korean Statistical Society
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• 제21권1호
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• pp.1-13
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• 1992

This article deals with variable selection problem under a newly formed predictive heteroscedastic discriminant rule that accounts for mulitple homogeneous covariance matrices across the K multivariate normal populations. A general version of predictive discriminant rule, a variable selection criterion, and a criterion for stopping with further selection are suggested. In a simulation study the practical utilities of those considered are demonstrated.

• Journal of the Korean Statistical Society
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• 제25권1호
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• pp.81-94
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• 1996

This paper suggests a new criterion for testing the general linear hypothesis about coefficients in multivariate growth curve model. It is developed from a Bayesian point of view using the highest posterior density region methodology. Likelihood ratio test criterion(LRTC) by Khatri(1966) results as an approximate special case. It is shown that under the simple case of vague prior distribution for the multivariate normal parameters a LRTC-like criterion results; but the degrees of freedom are lower, so the suggested test criterion yields more conservative test than is warranted by the classical LRTC, a result analogous to that of Berger and Sellke(1987). Moreover, more general(non-vague) prior distributions will generate a richer class of tests than were previously available.