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 \(\gamma \) which is defined by using Hadamard product of observation vectors, and propose an estimate of \(\gamma \) which is well defined when \(p>N\). 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
