• 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.

• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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• pp.587-592
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• 2009

The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.

• 대한예방의학회:학술대회논문집
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• 1994.02b
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• pp.154-157
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• 1994

The evaluation of diagnostic tests attempts to obtain one or more statistical parameters which can indicate the intrinsic diagnostic utility of a test. Sensitivity. specificity and predictive value are not appropriate for this use. The likelihood ratio has been proposed as a useful measure when using a test to diagnose one of two disease states (e.g. disease present or absent). In this paper, we generalize the likelihood ratio concept to a situation in which the goal is to diagnose one of several non-overlapping disease states. A formula is derived to determine the post-test probability of a specific disease state. The post-test odds are shown to be related to the pre-test odds of a disease and to the usual likelihood ratios derived from considering the diagnosis between the target diagnosis and each alternate in turn. Hence, likelihood ratios derived from comparing pairs of diseases can be used to determine test utility in a multiple disease diagnostic situation.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.71-78
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• 2018

In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.

• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.93-101
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• 2003

This paper deals with testing the equality of the coefficients of variation in two inverse Gaussian populations. The likelihood ratio, Lagrange-multiplier and Wald tests are presented. Monte-Carlo simulations are performed to compare the powers of these tests. In a simulation study, the likelihood ratio test appears to be consistently more powerful than the Lagrange-multiplier and Wald tests when sample size is small. The powers of all the tests tend to be similar when sample size increases.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.219-227
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• 2001

Another approach (multi-parameter measurement method) of interlaboratory studies of test methods is presented. When the unrestricted normal likelihood for the fixed latent variable model is unbounded, we propose a me쇙 of restricting the parameter space by formulating realistic alternative hypothesis under which the likelihood is bounded. A simulation study verified the claim of conservatism of level of significance based on assumptions about central chi-square distributed test statistics and on Bonferroni approximations. We showed a randomization approach that furnished empirical significance levels would be better than a Bonferroni adjustment.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.697-706
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• 2012

An Agresti-Coull type test is considered for the difference of binomial proportions in two doubly sampled data subject to common false-positive error. The performance of the test is compared with likelihood-based tests. The Agresti-Coull test has many desirable properties in that it can approximate the nominal significance level well, and has comparable power performance with a computational advantage.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.417-425
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• 2013

We consider an extended version of a logarithmic series distribution and discuss the estimation of its parameters by the method of moments and the method of maximum likelihood. Test procedures are suggested to test the significance of the additional parameter of this distribution and all procedures are illustrated with the help of real life data sets. In addition, a simulation study is conducted to assess the performance of the estimators.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.967-976
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• 1999

In this paper we study the Hellinger distance based goodness-of-fit tests that are analogs of likelihood ratio tests. The minimum Hellinger distance estimator (MHDE) in normal models provides an excellent robust alternative to the usual maximum likelihood estimator. Our simulation results show that the Hellinger deviance test (Simpson 1989) based goodness-of-fit test is robust when data contain outliers. The proposed hellinger deviance test(Simpson 1989) is a more direcct method for obtaining robust inferences than an automated outlier screen method used before the likelihood ratio test data analysis.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.397-405
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• 1997

Recently maximum likelihood estimators using unconditional likelihood function are used for testing unit roots. When one wants to use this method the determinant term of initial values in the multivariate unconditional likelihood function produces a complicated function of the elements in the coefficient matrix and variance matrix. In this paper an approximation of the determinant term is calculated and based on this aproximation an approximated unconditional likelihood function is calculated. The approximated unconditional maximum likelihood estimators can be used to test for unit roots. When multivariate process has one unit root the limiting distribution obtained by this method and the limiting distribution using exact unconditional likelihood function are the same.