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Testing normality in any dimension by Fourier methods in a multivariate Stein equation

Ebner, B.; Henze, N.; Strieder, D.


We study a novel class of affine-invariant and consistent tests for multivariate normality. The tests are based on a characterization of the standard d-variate normal distribution by way of the unique solution of an initial value problem connected to a partial differential equation, which is motivated by a multivariate Stein equation. The test criterion is a suitably weighted L2-statistic. We derive the limit distribution of the test statistic under the null hypothesis as well as under contiguous and fixed alternatives to normality. A consistent estimator of the limiting variance under fixed alternatives, as well as an asymptotic confidence interval of the distance of an underlying alternative with respect to the multivariate normal law, is derived. In simulation studies, we show that the tests are strong in comparison with prominent competitors and that the empirical coverage rate of the asymptotic confidence interval converges to the nominal level. We present a real data example and also outline topics for further research.

Verlagsausgabe §
DOI: 10.5445/IR/1000140705
Veröffentlicht am 06.12.2021
DOI: 10.1002/cjs.11670
Zitationen: 3
Web of Science
Zitationen: 3
Zitationen: 7
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0319-5724, 1708-945X
KITopen-ID: 1000140705
Erschienen in Canadian Journal of Statistics
Verlag John Wiley and Sons
Band 50
Heft 3
Seiten 992-1033
Vorab online veröffentlicht am 18.11.2021
Nachgewiesen in Web of Science
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