• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.479-488
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• 1999

Moore and Stubblebine(1981) suggested a chi-square test for multivariate normality based on cell counts calculated from the sample Mahalanobis distances. They derived the limiting distribution of the test statistic only when equiprobable cells are employed. Using conditional limit theorems, we derive the limiting distribution of the statistic as well as the asymptotic normality of the cell counts. These distributions are valid even when equiprobable cells are not employed. We finally apply this method to a real data set.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.939-946
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• 1999

We propose methods for detecting influential observations that have a large influence on the likelihood ratio test statistic for the multivariate Behrens-Fisher problem. For this purpose we derive the influence curve and the derivative influence of the likelihood ratio test statistic. An illustrative example is given to show the effectiveness of the proposed methods on the identification of influential observations.

• Journal of the Korean Data and Information Science Society
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• v.23 no.5
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• pp.1037-1044
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• 2012

Multivariate control charts for effectively monitoring every component in the dispersion matrix of multivariate normal process are considered. Through the numerical results, we noticed that the multivariate control charts based on sample statistic $V_i$ by Hotelling or $W_i$ by Alt do not work effectively when the correlation coefficient components in dispersion matrix are increased. We propose a combined procedure monitoring every component of dispersion matrix, which operates simultaneously both control charts, a chart controlling variance components and a chart controlling correlation coefficients. Our numerical results show that the proposed combined procedure is efficient for detecting changes in both variances and correlation coefficients of dispersion matrix.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1429-1433
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• 2009

The likelihood distance for the joint distribution of two multivariate normal distributions with common covariance matrix is explicitly derived. It is useful for identifying outliers which do not follow the joint multivariate normal distribution with common covariance matrix. The likelihood distance derived here is a good ground for the use of a generalized Wilks statistic in influence analysis of two multivariate normal data.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.385-392
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• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• International Journal of Reliability and Applications
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• v.6 no.1
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• pp.53-64
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• 2005

In this paper, we propose a nonparametric test procedure for the multivariate, grouped and right censored data for two sample problem. For the construction of the test statistic, we use the linear rank statistics for each component and apply the permutation principle for obtaining the null distribution. For the large sample case, the asymptotic distribution is derived under the null hypothesis with the additional assumption that two censoring distributions are also equal. Finally, we illustrate our procedure with an example and discuss some concluding remarks. In appendices, we derive the expression of the covariance matrix and prove the asymptotic distribution.

• Journal of Integrative Natural Science
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• v.5 no.3
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• pp.151-156
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• 2012

Because of the equivalence between control chart procedures and hypothesis testing, we propose to use likelihood ratio test (LRT) statistic $Z_i^2$ as the multivariate control statistic for simultaneous monitoring means of the multivariate normal process. Properties and comparisons of the proposed control charts are explored and conducted for matched fixed sampling interval (FSI) and variable sampling interval (VSI) with two sampling interval charts. The result of numerical comparisons shows that EWMA chart with two sampling interval procedure is more efficient than the corresponding FSI chart for small or moderate changes. When large shift of the process has occurred, we also found that Shewhart chart is more efficient than EWMA chart.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1191-1200
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under two non-normal distributions.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.319-332
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• 1997

The application of multivariate linear rank statistics to data with item nonresponse is considered. Only a modest extension of the complete data techniques is required when the missing data may be thought of as a random sample, and an appropriate modification of the covariances is derived. A proof of the asymptotic multivariate normality is given. A review of some related results in the literature is presented and applications including longitudinal and repeated measures designs are discussed.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.203-212
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under two non-normal distributions.