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A Note on Measures of Multivariate Kurtosis
Biometrical Journal, 1989AbstractWe propose a measure of multivariate kurtosis suggested from Mardia's measure of multivariate skewness b1,p, and examine its relationship both to Mardia's measure of multivariate kurtosis b2,p, and to a smooth test of multivariate kurtosis Ǔ42.
James Koziol
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Multivariate kurtosis in L1-sense
Statistics & Probability Letters, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Averous, Jean, Meste, Michel
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The null distribution of multivariate kurtosis
Communications in Statistics - Simulation and Computation, 1983The paper introduces a x2-approximation to multivariate kurtosis b2,punder normality. It requires calculating the third moment of b2,pwhich is obtained. We compare the approximation with simulated percentage points and the normal approximation, and find it to be adequate for p=l and 2.
K.V. Mardia, M. Kanazawa
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Stabilizing the Performance of Kurtosis Estimator of Multivariate Data
Communications in Statistics - Simulation and Computation, 2012The estimation of the kurtosis parameter of the underlying distribution plays a central role in many statistical applications. The central theme of the article is to improve the estimation of the kurtosis parameter using a priori information. More specifically, we consider the problem of estimating kurtosis parameter of a multivariate population when ...
S. Ejaz Ahmed +2 more
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Multivariate normality test using normalizing transformation for Mardia’s multivariate kurtosis
Communications in Statistics - Simulation and Computation, 2019AbstractMultivariate skewness and kurtosis were defined by Mardia. However, the distribution of multivariate normality test statistics based on skewness and kurtosis is only obtainable for large sa...
Rie Enomoto +3 more
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Mardia's Multivariate Kurtosis with Missing Data
Multivariate Behavioral Research, 2004Mardia's measure of multivariate kurtosis has been implemented in many statistical packages commonly used by social scientists. It provides important information on whether a commonly used multivariate procedure is appropriate for inference. Many statistical packages also have options for missing data. However, there is no procedure for applying Mardia'
Ke-Hai Yuan +2 more
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Estimating p-values for Mardia’s coefficients of multivariate skewness and kurtosis
Computational Statistics, 2002This paper deals with a test of multivariate normality based on Mardia's estimates of multivariate skewness \(z_1\) and kurtosis \(z_2\). While the properly normalized statistics \(z_1\) and \(z_2\) asymptotically have a \(\chi^2\) and normal distribution, respectively, Mardia's test does not perform well in small sample cases. A Monte-Carlo method for
Douglas G. Bonett +2 more
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The asymptotic behavior of a variant of multivariate kurtosis
Communications in Statistics - Theory and Methods, 1994Let be independent identically distributed random d-dimensional column vectors with arithmetic mean [Xbar] n and empirical covariance matrix S n. Apart from the celebrated kurtosis measure of Mardia, there has been recent interest in the variant which formally constitutes a closer analogue to the multivariate skewness measure , than b2,d . We show that,
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Journal of Statistical Computation and Simulation, 1992
The examination of coefficients of multivariate skewness and kurtosis is one of the more commonly used techniques for assessing multivariate normality (MVN). In this article, several tests for MVN based on these coefficients are compared via Monte Carlo simulation.
Ronald L. Horswell, Stephen W. Looney
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The examination of coefficients of multivariate skewness and kurtosis is one of the more commonly used techniques for assessing multivariate normality (MVN). In this article, several tests for MVN based on these coefficients are compared via Monte Carlo simulation.
Ronald L. Horswell, Stephen W. Looney
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Measures of multivariate skewness and kurtosis for tests of nonnormality
Statistical Papers, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lütkepohl, H., Theilen, B.
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