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Measures of multivariate skewness and kurtosis with applications
Abstract
Measures of multivariate skewness and kurtosis are developed by extending certain studies on robustness of the t statistic. These measures are shown to possess desirable properties. The asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test of multivariate normality is proposed. The effect of nonnormality on the size of the one-sample Hotelling's T2 test is studied empirically with the help of these measures, and it is found that Hotelling's T2 test is more sensitive to the measure of skewness than to the measure of kurtosis.
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Cites
An analysis of variance test for normality (complete samples)
SHAPIRO, S. S., & WILK, M. B. (1965) · Biometrika · doi:10.1093/biomet/52.3-4.591 · Cited by 23,480
Cited by
Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000) · Cognitive Psychology · doi:10.1006/cogp.1999.0734 · Cited by 15,798
Practical issues in structural modeling
BENTLER, P. M., & CHOU, C.-P. (1987) · Sociological Methods & Research · doi:10.1177/0049124187016001004 · Cited by 5,804
Wetzels, M., Odekerken-Schröder, G., & van Oppen, C. (2009) · MIS Quarterly · doi:10.2307/20650284 · Cited by 4,944
Principles and practice in reporting structural equation analyses.
McDonald, R. P., & Ho, M.-H. R. (2002) · Psychological Methods · doi:10.1037/1082-989x.7.1.64 · Cited by 4,734
Statistical difficulties of detecting interactions and moderator effects.
McClelland, G. H., & Judd, C. M. (1993) · Psychological Bulletin · doi:10.1037/0033-2909.114.2.376 · Cited by 3,270
Metadata
- Authors
- MARDIA, K. V.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1970
- Volume
- 57
- Issue
- 3
- Pages
- 519-530
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2000031724
- Cited by
- 4,792
- References
- 1
- FWCI
- 1.39
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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