• 한국수학교육학회지시리즈A:수학교육
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• 제55권2호
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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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• 제23권6호
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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.

• Communications for Statistical Applications and Methods
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• 제25권4호
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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.

• 응용통계연구
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• 제18권3호
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• pp.673-687
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• 2005

표본조사에서 이용하는 모수 추론 방법인 설계기반추론과 모형기반추론을 고찰하였다. 설계기반추론은 확률화 원리에 기초를 두고 있는 반면 모형기반추론은 가정한 모형에서 조건부 원리와 우도 원리에 바탕을 두고 있다. 두 추론은 서로 다른 이론적 근거를 사용하기 때문에 이론적 기초에 관한 논쟁이 오래 전부터 있어 왔으며 지금도 진행되고 있다. 이 논문에서는 두 추론 사이에 진행되었던 논쟁의 초점을 살펴보았고 몇 가지 관점에서 두 추론의 장단점을 비교하였다.

• Communications for Statistical Applications and Methods
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• 제23권6호
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• pp.479-496
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• 2016

In this survey, we present a modified inverse moment estimation of parameters and its applications. We use a specific model to demonstrate its principle and how to apply this method in practice. The estimation of unknown parameters is considered. A necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters is obtained for the classical maximum likelihood estimation. Inverse moment and modified inverse moment estimators are proposed and their properties are studied. Monte Carlo simulations are conducted to compare the performances of these estimators. As far as the biases and mean squared errors are concerned, modified inverse moment estimator works the best in all cases considered for estimating the unknown parameters. Its performance is followed by inverse moment estimator and maximum likelihood estimator, especially for small sample sizes.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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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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• 제13권2호
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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.

• 응용통계연구
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• 제22권5호
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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)

• 음성과학
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• 제11권4호
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• pp.43-52
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• 2004

Model parameters in HMM based speech recognition systems are normally estimated using Maximum Likelihood Estimation(MLE). The MLE method is based mainly on the principle of statistical data fitting in terms of increasing the HMM likelihood. The optimality of this training criterion is conditioned on the availability of infinite amount of training data and the correct choice of model. However, in practice, neither of these conditions is satisfied. In this paper, we propose a training algorithm, MCE(Minimum Classification Error), to improve the performance of a speech recognizer detecting mispronunciation of a foreign language. During the conventional MLE(Maximum Likelihood Estimation) training, the model parameters are adjusted to increase the likelihood of the word strings corresponding to the training utterances without taking account of the probability of other possible word strings. In contrast to MLE, the MCE training scheme takes account of possible competing word hypotheses and tries to reduce the probability of incorrect hypotheses. The discriminant training method using MCE shows better recognition results than the MLE method does.

• Journal of the Korean Data and Information Science Society
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• 제20권1호
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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.