EconPapers    
Economics at your fingertips  
 

Extreme smoothing and testing for multivariate normality

Norbert Henze

Statistics & Probability Letters, 1997, vol. 35, issue 3, 203-213

Abstract: Recently, Bowman and Foster (1993) proposed to base a test for multivariate normality on a L2 distance between a nonparametric kernel density estimator and the parametric density estimator under normality, applied to the empirically standardized data. We show that, for a fixed bandwidth (not depending on the sample size), the test of Bowman and Foster is a member of the class of invariant and universally consistent procedures suggested by Henze and Zirkler (1990). Moreover, we identify and study the tests for multivariate normality obtained by letting the bandwidth tend to zero and to infinity. While the former test statistic is based solely on the Euclidean norm of the standardized data, letting the bandwidth tend to infinity yields a weighted sum of Mardia's time-honoured measure of multivariate skewness and a sample version of a recently introduced skewness measure of Móri, Rohatgi and Székely (1993).

Keywords: Multivariate; skewness; Smoothing; Elliptically; symmetric; distributions; Test; for; multivariate; normality (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(97)00015-1
Full text for ScienceDirect subscribers only

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:eee:stapro:v:35:y:1997:i:3:p:203-213

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().

 
Page updated 2025-03-19
Handle: RePEc:eee:stapro:v:35:y:1997:i:3:p:203-213