TY - JOUR
T1 - Sub-dimensional Mardia measures of multivariate skewness and kurtosis
AU - Chowdhury, Joydeep
AU - Dutta, Subhajit
AU - Arellano-Valle, Reinaldo B.
AU - Genton, Marc G.
N1 - KAUST Repository Item: Exported on 2022-09-14
Acknowledgements: This research was supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia. We thank the associate editor and the anonymous reviewers for their helpful comments and suggestions.
PY - 2022/8/9
Y1 - 2022/8/9
N2 - The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution. Consequently, testing procedures based on these measures may fail to detect skewness or kurtosis present in a sub-dimension of the multivariate distribution. We introduce sub-dimensional Mardia measures of multivariate skewness and kurtosis, and investigate the information they convey about all sub-dimensional distributions of some symmetric and skewed families of multivariate distributions. The maxima of the sub-dimensional Mardia measures of multivariate skewness and kurtosis are considered, as these reflect the maximum skewness and kurtosis present in the distribution, and also allow us to identify the sub-dimension bearing the highest skewness and kurtosis. Asymptotic distributions of the vectors of sub-dimensional Mardia measures of multivariate skewness and kurtosis are derived, based on which testing procedures for the presence of skewness and of deviation from Gaussian kurtosis are developed. The performances of these tests are compared with some existing tests in the literature on simulated and real datasets.
AB - The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution. Consequently, testing procedures based on these measures may fail to detect skewness or kurtosis present in a sub-dimension of the multivariate distribution. We introduce sub-dimensional Mardia measures of multivariate skewness and kurtosis, and investigate the information they convey about all sub-dimensional distributions of some symmetric and skewed families of multivariate distributions. The maxima of the sub-dimensional Mardia measures of multivariate skewness and kurtosis are considered, as these reflect the maximum skewness and kurtosis present in the distribution, and also allow us to identify the sub-dimension bearing the highest skewness and kurtosis. Asymptotic distributions of the vectors of sub-dimensional Mardia measures of multivariate skewness and kurtosis are derived, based on which testing procedures for the presence of skewness and of deviation from Gaussian kurtosis are developed. The performances of these tests are compared with some existing tests in the literature on simulated and real datasets.
UR - http://hdl.handle.net/10754/673945
UR - https://linkinghub.elsevier.com/retrieve/pii/S0047259X22000859
UR - http://www.scopus.com/inward/record.url?scp=85135694671&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2022.105089
DO - 10.1016/j.jmva.2022.105089
M3 - Article
SN - 1095-7243
VL - 192
SP - 105089
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -