• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1097-1102
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• 2009

Classification of subjects with unknown distribution in small sample size setup may involve order-restricted constraints in multivariate parameter setups. Those problems makes optimality of conventional likelihood ratio based statistical inferences not feasible. Fortunately, Roy (1953) introduced union-intersection principle(UIP) which provides an alternative avenue. Redescending M-estimator along with that principle yields a considerably appropriate robust testing procedure. Furthermore, conditionally distribution-free test based upon exact permutation theory is used to generate p-values, even in small sample. Applications of this method are illustrated in simulated data and read data example (Lobenhofer et al., 2002)

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.457-470
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• 2003

The comparison of two or more Lorenz curves of Pareto distributions of first kind under arbitrary order restriction is studied. The problem is turned out to be a statistical inference problem concerning scale parameters under order restriction. We assume that the location parameters of Palate distributions are completely unknown. In this paper the maximum likelihood estimation and likelihood ratio tests for and against order restriction are proposed.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.109-114
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• 2003

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter, which is peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose nonparametric maximum likelihood estimator of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.303-312
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• 2004

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter. This is the peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose non parametric maximum likelihood estimators of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.335-347
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• 2007

Two new types of positive biasedness, which are closely related to Type III positive biasedness (Yanagimoto and Sibuya, 1972), are proposed. We call these near Type III positive biasedness. Though no implication between Type II and near Type III biasedness exists, near Type III seems to be less restrictive than Type II biasedness. Constrained maximum likelihood estimates of distribution functions under near Type III positive bisedness are obtained. The likelihood ratio tests of symmetry against new positive biasedness restrictions are proposed. A small simulation study is conducted to compare the performance of the tests.

• Communications for Statistical Applications and Methods
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• v.25 no.5
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• pp.559-568
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• 2018

Gene classification can involve complex order-restricted inference. Examining gene expression pattern across groups with order-restriction makes standard statistical inference ineffective and thus, requires different methods. For this problem, Roy's union-intersection principle has some merit. The M-estimator adjusting for outlier arrays in a microarray study produces a robust test statistic with distribution-insensitive clustering of genes. The M-estimator in conjunction with a union-intersection principle provides a nonstandard robust procedure. By exact permutation distribution theory, a conditionally distribution-free test based on the proposed test statistic generates corresponding p-values in a small sample size setup. We apply a false discovery rate (FDR) as a multiple testing procedure to p-values in simulated data and real microarray data. FDR procedure for proposed test statistics controls the FDR at all levels of ${\alpha}$ and ${\pi}_0$ (the proportion of true null); however, the FDR procedure for test statistics based upon normal theory (ANOVA) fails to control FDR.

• Communications for Statistical Applications and Methods
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• v.15 no.1
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• pp.13-26
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• 2008

Inference on the present data will be more reliable when the data arising from previous similar studies are available. The data arising from previous studies are referred as historical data. The power prior is defined by the likelihood function based on the historical data to the power $a_0$, where $0\;{\le}\;a_0\;{\le}\;1$. The power prior is a useful informative prior for Bayesian inference such as model selection and model comparison. We utilize the historical data to perform multiple comparison in the one-way ANOVA model. We demonstrate our results with some simulated datasets under a simple order restriction between the treatments.

• The Korean Journal of Applied Statistics
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• v.31 no.3
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• pp.409-416
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• 2018

Significant research has been conducted in the financial sector on the behavior of investors in the stock market. In this paper, we directly measure the degree of interest using the ranking of the frequency mentioned in the stock message board operated by Daum Communications Corp. and test the fact that the higher ranking of the frequency results in the higher stock returns in order to investigate the attention effect on the stock returns in the Korean stock market. We also propose and apply the likelihood ratio test procedure for order restricted hypotheses in order to test the attention effect. The test results shows that the higher rank in the frequency mentioned in the message board is related to stock returns (p-value < $10^{-6}$). Therefore, we conclude that an investors' attention effects exist in the Korean stock market.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.185-191
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• 1997

Bayesian estimation of multinomial and Poisson parameters under starshped restriction is considered. Most Bayesian estimations in order restricted statistical inference require the high-dimensional integration which is very difficult to evaluate. Monte Carlo integration and Gibbs sampling are among alternative methods. The Bayesian estimation considered in this paper requires only evaluation of incomplete beta functions which are extensively tabulated.

• Journal of the Korea Society of Computer and Information
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• v.3 no.3
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• pp.55-61
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• 1998

The learning order of teaching materials to be a learning data in CAI is arranged from an easy item to a difficult one A learning in not necessary to be learned arranged this order. Actually the learning is done by the rules of trial and error on the sequences of an arrangement among items. In this papers, the constructed is modelled by the fuzzy inference after leaning the understanding on items by the intelligent CAI through the rile of trial and error of fuzziness. Given the difference of leaning and understanding, the leaning model is quantified by the order relationship among items and by the rules of fuzzy inference. The rule of trial and error of learning is restricted to the treatment of CAL system minimizing the rules of inference.