• Journal of the Korean Data and Information Science Society
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• 제17권4호
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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.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2006년도 PROCEEDINGS OF JOINT CONFERENCEOF KDISS AND KDAS
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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.

• Journal of the Korean Data and Information Science Society
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• 제15권2호
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• pp.423-430
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• 2004

We provide the exact form of a Rao-Robson version of the chi-squared test of multivariate normality suggested by Park(2001). This test is easy to apply in practice since it is easily computed and has a limiting chi-squared distribution under multivariate normality. A self-contained formal argument is provided that it has the limiting chi-squared distribution. A simulation study is provided to study the accuracy, in finite samples, of the limiting distribution. Finally, a simulation study in a nonnormal distribution is conducted in order to compare the power of our test with those of other popular normality tests.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.765-777
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• 2003

In this paper, we investigate some measures as tests of multivariate normality based on principal components. The idea was proposed by Srivastava and Hui(1987). They generalized Shapiro-Wilk statistic for multi variate cases. We show the null distributions of the statistics do not depend on the unknown parameters and mention the asymptotic null distributions. Also power performance of the tests are assessed in a Monte Carlo study.

• Journal of the Korean Data and Information Science Society
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• 제17권1호
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• pp.221-231
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• 2006

A chi-squared test of multivariate normality is suggested which is oriented for detecting deviations from elliptical symmetry. We derive the limiting distribution of the test statistic via a central limit theorem on empirical processes. 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 a non-normal distribution.

• Journal of the Korean Data and Information Science Society
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• 제17권1호
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• pp.115-122
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• 2006

A test is suggested for detecting deviations from both multivariate normality and independence. This test can be used for assessing the normality and independence of univariate time series residuals. We derive the limiting distribution of the test statistic and a simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we apply our method to a real data of time series.

• 응용통계연구
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• 제17권3호
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• pp.507-518
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• 2004

Malkovich & Afifi (1973)는 합교원리 (union-intersection principle)를 이용하여 왜도와 첨도를 다변량으로 일반화하였으나 이는 자료의 차원이 클 경우에는 사용이 용이하지 않다. 본 논문에서는 이러한 단점을 보완하는 이들의 근사통계량을 제안한다. 그리고 제안된 근사통계량, Malkovich & Afifi (1973)의 통 계 량, Mardia(1970)의 왜도와 첨도의 검 정력을 모의실험을 통하여 비교한다.

• Communications for Statistical Applications and Methods
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• 제28권5호
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• pp.463-475
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• 2021

Desgagné and de Micheaux (2018) proposed an alternative univariate normality test to the Jarque-Bera test. The proposed statistic is based on the sample second power skewness and kurtosis while the Jarque-Bera statistic uses sample Pearson's skewness and kurtosis that are the third and fourth standardized sample moments, respectively. In this paper, we generalize their statistic to a multivariate version based on orthogonalization or an empirical standardization of data. The proposed multivariate statistic follows chi-squared distribution approximately. A simulation study shows that the proposed statistic has good control of type I error even for a very small sample size when critical values from the approximate distribution are used. It has comparable power to the multivariate version of the Jarque-Bera test with exactly the same idea of the orthogonalization. It also shows much better power for some mixed normal alternatives.

• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.1013-1021
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• 2003

Huffer and Park (2002) proposed a chi-squared test for multivariate structure. Their test detects the deviation of data from mutual independence or multivariate normality. We will compute the Rao-Robson chi-squared version of the test, which is easy to apply in practice since it has a limiting chi-squared distribution. We will provide a self-contained argument that it has a limiting chi-squared distribution. We study the accuracy in finite samples of the limiting distribution. We finally compare the power of our test with those of other popular normality tests in an application to a real data.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.71-86
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• 2005

Testing for normality has always been an important part of statistical methodology. In this paper a test statistic for multivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is representable as the supremum over an index set of the integral of a suitable Gaussian process.