• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.563-574
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• 2016

In this study, we propose several simultaneous tests to detect the difference between means and variances for the two-sample problem when the underlying distribution is normal. For this, we apply the likelihood ratio principle and propose a likelihood ratio test. We then consider a union-intersection test after identifying the likelihood statistic, a product of two individual likelihood statistics, to test the individual sub-null hypotheses. By noting that the union-intersection test can be considered a simultaneous test with combination function, also we propose simultaneous tests with combination functions to combine individual tests for each sub-null hypothesis. We apply the permutation principle to obtain the null distributions. We then provide an example to illustrate our proposed procedure and compare the efficiency among the proposed tests through a simulation study. We discuss some interesting features related to the simultaneous test as concluding remarks. Finally we show the expression of the likelihood ratio statistic with a product of two individual likelihood ratio statistics.

• The Mathematical Education
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• v.55 no.2
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• pp.193-208
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• 2016

This study analyzes the likelihood principle and elicits an educational implication. As a result of analysis, this study shows that Frequentist and Bayesian interpret the principle differently by assigning different role to that principle from each other. While frequentist regards the principle as 'the principle forming a basis for statistical inference using the likelihood ratio' through considering the likelihood as a direct tool for statistical inference, Bayesian looks upon the principle as 'the principle providing a basis for statistical inference using the posterior probability' by looking at the likelihood as a means for updating. Despite this distinction between two methods of statistical inference, two statistics schools get clues to compromise in a regard of using frequency prior probability. According to this result, this study suggests the statistics education that is a help to building of students' critical eye by their comparing inferences based on likelihood and posterior probability in the learning and teaching of updating process from frequency prior probability to posterior probability.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.329-339
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• 2018

In this study, we propose tests for equality of several variances with the normality assumption. First of all, we propose the likelihood ratio test by applying the permutation principle. Then by using the p-values for the pairwise tests between variances and combination functions, we propose combination tests. We apply the permutation principle to obtain the overall p-values. Also we review the well- known test statistics for the completion of our discussion and modify a statistic with the p-values. Then we illustrate proposed tests by numerical and simulated data and compare their efficiency with the reviewed ones through a simulation study by obtaining empirical p-values. Finally, we discuss some interesting features related to the resampling methods and tests for equality among several variances.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.159-164
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• 2000

In the study of the isotonic regression problem, several procedures for testing the homogeneity of a normal mean vector versus order restricted alternatives have been proposed since Barlow's trial(1972). In this paper, we consider the problem of testing the equality of two order restricted normal mean vectors based on the likelihood ratio principle.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.409-418
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• 2006

We propose a nonparametric test procedure for the K-sample problem with grouped data. We construct the test statistics using the scores derived for the linear model based on likelihood ratio principle and obtain asymptotic distribution. Also we illustrate our procedure with an example. Finally we discuss some concluding remarks.

• 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 the Korean Data and Information Science Society
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• v.20 no.1
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• pp.237-250
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• 2009

We consider a nonparametric test procedure for the multi-sample problem with grouped data. We construct the test statistics based on the scores obtained from the likelihood ratio principle and derive the limiting distribution under the null hypothesis. Also we illustrate our procedure with an example and obtain the asymptotic properties under the Pitman translation alternatives. Also we discuss some concluding remarks. Finally we derive the covariance between components in the Appendix.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.137-143
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• 2011

The classification of subjects with unknown distribution in a small sample size often involves order-restricted constraints in multivariate parameter setups. Those problems make the optimality of a conventional likelihood ratio based statistical inferences not feasible. Fortunately, Roy (1953) introduced union-intersection principle(UIP) which provides an alternative avenue. Multivariate linear rank statistics along with that principle, yield a considerably appropriate robust testing procedure. Furthermore, conditionally distribution-free test based upon exact permutation theory is used to generate p-values, even in a small sample. Applications of this method are illustrated in a real microarray data example (Lobenhofer et al., 2002).

• Proceedings of the Korean Information Science Society Conference
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• 1999.10b
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• pp.57-59
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• 1999

본 논문에서는 최대 엔트로피 원리에 기반한 문서 분류기의 학습을 제안한다. 최대 엔트로피 기법은 자연언어 처리에서 언어 모델링(Language Modeling), 품사 태깅 (Part-of-Speech Tagging) 등에 널리 사용되는 방법중의 하나이다. 최대 엔트로피 모델의 효율성을 위해서는 자질 선정이 중요한데, 본 논문에서는 자질 집합의 선택을 위한 기준으로 chi-square test, log-likelihood ratio, information gain, mutual information 등의 방법을 이용하여 실험하고, 전체 후보 자질에 대한 실험 결과와 비교해 보았다. 데이터 집합으로는 Reuters-21578을 사용하였으며, 각 클래스에 대한 이진 분류 실험을 수행하였다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.205-208
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• 2005

We have fuzzy hypotheses testing from Bayesian statistics with ideas from fuzzy sets theory to generalize Bayesian methods both for samples of fuzzy data and for prior distributions with non-precise parameters. Appling the principle of agreement index, the posterior odds ratio in the favor of hypotheses $H_0$ is equal to product of the fuzzy odds ratio and the fuzzy likelihood ratio. If the Posterior odds ratio exceeds the grade judgement, we accept the hypothesis $H_0$ for the degree.