A test for normality and independence based on characteristic function

Wiktor Ejsmont (), Bojana Milošević () and Marko Obradović ()
Additional contact information
Wiktor Ejsmont: Wroclaw University of Science and Technology
Bojana Milošević: Faculty of Mathematics
Marko Obradović: Faculty of Mathematics

Statistical Papers, 2023, vol. 64, issue 6, No 3, 1889 pages

Abstract: Abstract In this article we prove a generalization of the Ejsmont characterization (Ejsmont in Stat Probab Lett 114:1–5, 2016) of the multivariate normal distribution. Based on it, we propose a new test for independence and normality. The test uses an integral of the squared modulus of the difference between the product of empirical characteristic functions and some constant. Special attention is given to the case of testing for univariate normality in which we derive the test statistic explicitly in terms of Bessel function and explore asymptotic properties. The simulation study also includes the cases of testing for bivariate and trivariate normality and independence, as well as multivariate normality. We show the quality performance of our test in comparison to some popular powerful competitors. The practical application of the proposed normality and independence test is discussed and illustrated using a real dataset.

Keywords: Characterization; Multivariate normal distribution; Goodness-of-fit test; Empirical characteristic function; Primary: 62H15; Secondary: 62E10 (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-022-01365-1 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:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01365-1

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-022-01365-1

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

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