• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.195-203
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• 1996

A bootstrap method is used to correct the apparent downward bias of a naive plug-in bootstrap model selection criterion, which is shown to enjoy a high degree of accuracy. Comparison of bootstrap method with the asymptotic method is made through an illustrative example.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.233-238
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• 2003

Goodness of fit test statistics based on the information discrepancy have been shown to perform very well (Vasicek 1976, Dudewicz and van der Meulen 1981, Chandra et al 1982, Gohkale 1983, Arizona and Ohta 1989, Ebrahimi et al 1992, etc). Although the test is well defined for the non-censored case, censored case has not been discussed in the literature. Therefore we consider a goodness of fit test based on the partial Kullback-Leibler(KL) information with the type II censored data. We derive the partial KL information of the null distribution function and a nonparametric distribution function, and establish a goodness of fit test statistic. We consider the exponential and normal distributions and made Monte Calro simulations to compare the test statistics with some existing tests.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.125-134
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• 2014

Kullback-Leibler (KL) information is a measure of discrepancy between two probability density functions. However, several nonparametric density function estimators have been considered in estimating KL information because KL information is not well-defined on the empirical distribution function. In this paper, we consider the KL information of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF), and propose an EDF-based goodness of fit test statistic. We evaluate the performance of the proposed test statistic for an exponential distribution with Monte Carlo simulation. We also extend the discussion to the censored case.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.93-110
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• 1992

A model selection approach is used to find out whether the mean and the variance of a unique sample are different from the pre-specified values. Normal distribution is selected as an approximating model. Kullback-Leibler discrepancy comes out as a natural measure of discrepancy between the operating model and the approximating model. Several estimates of selection criterion are computed including AIC, TIC, and a coupleof bootstrap estimator of the selection criterion are considered according to the way of resampling. It is shown that a closed form expression is available for the parametric bootstrap estimated cirterion. A Monte Carlo study is provided to give a formal comparison when the operating family itself is normally distributed.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.289-303
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• 1998

For square contingency tables with ordered categories, Tomizawa (1995) considered two kinds of measures to represent the degree of departure from global symmetry, which means that the probability that an observation will fall in one of cells in the upper-right triangle of square table is equal to the probability that the observation falls in one of cells in the lower-left triangle of it. This paper proposes a generalization of those measures. The proposed measure is expressed by using Cressie and Read's (1984) power divergence or Patil and Taillie's (1982) diversity index. Special cases of the proposed measure include TomiBawa's measures. The proposed measure would be useful for comparing the degree of departure from global symmetry in several tables.