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Preoperative differentiation of primary vs. metastatic lumbar spine tumors: development and external validation of a multiparametric MRI-based radiomics nomogram. [PDF]

Front Oncol
Shen C, Yang S, Chen X, Feng Y, Song Y, Zhou J, Sun Y.   +6 more
europepmc   +1 more source

A new multivariate kurtosis and its asymptotic distribution

A new multivariate kurtosis and its asymptotic distribution
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Measures of multivariate skewness and kurtosis in high-dimensional framework

Measures of multivariate skewness and kurtosis in high-dimensional framework
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A Note on Measures of Multivariate Kurtosis

Biometrical Journal, 1989
AbstractWe 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 A Koziol
exaly   +2 more sources

On Multivariate Skewness and Kurtosis

Theory of Probability and Its Applications, 1994
Summary: Let \(X\) be a \(d\)-dimensional standardized random variable \(({\mathbf E}(X) = 0\), \(\text{cov}(X) = 1)\). Then for a multivariate analogue of skewness \(s = {\mathbf E}(\| X \|^ 2 X)\) and kurtosis \(k = {\mathbf E} XX^ T XX^ T - (d + 2)I\) we show that \(\| s\|^ 2 \leq \text{tr }k + 2d\). For infinitely divisible distributions, \(\| s\|^
Tamás F Mori
exaly   +4 more sources

Multivariate kurtosis in L1-sense

Statistics & Probability Letters, 1994
zbMATH 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, 1983
The 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, 2012
The 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, M. Hafidz Omar, Anwar H. Joarder   +2 more
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Mardia's Multivariate Kurtosis with Missing Data

Multivariate Behavioral Research, 2004
Mardia'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, Paul L. Lambert, Rachel T. Fouladi   +2 more
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