• Title, Summary, Keyword: likelihood ratio test

### Test procedures for the mean and variance simultaneously under normality

• Park, Hyo-Il
• 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.

### Likelihood ratio in estimating Chi-square parameter

• Rahman, Mezbahur
• 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.

### A note on the test for the covariance matrix under normality

• Park, Hyo-Il
• 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.

### ON TESTING THE EQUALITY OF THE COEFFICIENTS OF VARIATION IN TWO INVERSE GAUSSIAN POPULATIONS

• Choi, Byung-Jin;Kim, Kee-Young
• 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.

### Tests of Hypotheses in Multiple Samples based on Penalized Disparities

• Park, Chanseok;Ayanendranath Basu;Ian R. Harris
• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.347-366
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• 2001
• Robust analogues of the likelihood ratio test are considered for testing of hypotheses involving multiple discrete distributions. The test statistics are generalizations of the Hellinger deviance test of Simpson(1989) and disparity tests of Lindsay(1994), obtained by looking at a 'penalized' version of the distances; harris and Basu (1994) suggest that the penalty be based on reweighting the empty cells. The results show that often the tests based on the ordinary and penalized distances enjoy better robustness properties than the likelihood ratio test. Also, the tests based on the penalized distances are improvements over those based on the ordinary distances in that they are much closer to the likelihood ratio tests at the null and their convergence to the x$^2$ distribution appears to be dramatically faster; extensive simulation results show that the improvement in performance of the tests due to the penalty is often substantial in small samples.

### Influence Measures for the Likelihood Ratio Test on Independence of Two Random Vectors

• Jung, Kang-Mo
• 한국데이터정보과학회:학술대회논문집
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• pp.13-16
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• 2001
• We compare methods for detecting influential observations that have a large influence on the likelihood ratio test statistics that the two sets of variables are uncorrelated with one another. For this purpose we derive results of the deletion diagnostic, the influence function, the standardized influence matrix and the local influence. An illustrative example is given.

### Test and Estimation for Exponential Mean Change

• Kim, Jae-Hee
• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.421-427
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• 2008
• This paper deals with the problem of testing for the existence of change in mean and estimating the change-point when the data are from the exponential distributions. The likelihood ratio test statistic and Gombay and Horvath (1990) test statistic are compared in a power study when there exists one change-point in the exponential means. Also the change-point estimator using the likelihood ratio and the change-point estimators based on Gombay and Horvath (1990) statistic are compared for their detecting capability via simulation.

### Target Detection Performance in a Clutter Environment Based on the Generalized Likelihood Ratio Test (클러터 환경에서의 GLRT 기반 표적 탐지성능)

• Suh, Jin-Bae;Chun, Joo-Hwan;Jung, Ji-Hyun;Kim, Jin-Uk
• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.30 no.5
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• pp.365-372
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• 2019
• We propose a method to estimate unknown parameters(e.g., target amplitude and clutter parameters) in the generalized likelihood ratio test(GLRT) using maximum likelihood estimation and the Newton-Raphson method. When detecting targets in a clutter environ- ment, it is important to establish a modular model of clutter similar to the actual environment. These correlated clutter models can be generated using spherically invariant random vectors. We obtain the GLRT of the generated clutter model and check its detection probability using estimated parameters.

### Minimum Hellinger Distance Bsed Goodness-of-fit Tests in Normal Models: Empirical Approach

• Dong Bin Jeong
• 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.

### Likelihood Ratio Test for the Equality of Two Order Restricted Normal Mean Vectors

• Jeon Hyojin;Choi Sungsub
• Proceedings of the Korean Statistical Society Conference
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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.