Estimation of multivariate 3rd moment for high-dimensional data and its application for testing multivariate normality

Takayuki Yamada () and Tetsuto Himeno
Additional contact information
Takayuki Yamada: Kagoshima University
Tetsuto Himeno: Shiga University

Computational Statistics, 2019, vol. 34, issue 2, No 23, 941 pages

Abstract: Abstract This paper is concerned with the multivariate 3rd moment and its estimation. Mardia (Biometrika 57:519–530, 1970) and Srivastava (Stat Probab Lett 2:263–267, 1984) proposed the multivariate skewness and its estimator, independently. However, these estimators cannot be defined for the case in which the dimension p is larger than the sample size N. In this paper, we treat the multivariate 3rd moment $$\gamma $$ γ which is defined by using Hadamard product of observation vectors, and propose an estimate of $$\gamma $$ γ which is well defined when $$p>N$$ p > N . Based on the estimator, we propose a new test for multivariate normality. Under the null hypothesis, the test statistic is asymptotically standard normal, which is supported by Monte Carlo simulations. We calculate some empirical powers to see the performance of the test.

Keywords: Multivariate 3rd moment; Hadamard product; Testing multivariate normality (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00180-018-00865-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-018-00865-9

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-018-00865-9

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().