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Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces

Dörr, Philip; Ebner, Bruno; Henze, Norbert

We study a novel class of affine invariant and consistent tests for normality in any dimension in an i.i.d.‐setting. The tests are based on a characterization of the standard d‐variate normal distribution as the unique solution of an initial value problem of a partial differential equation motivated by the harmonic oscillator, which is a special case of a Schrödinger operator. We derive the asymptotic distribution of the test statistics under the hypothesis of normality as well as under fixed and contiguous alternatives. The tests are consistent against general alternatives, exhibit strong power performance for finite samples, and they are applied to a classical data set due to R.A. Fisher. The results can also be used for a neighborhood‐of‐model validation procedure.

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Verlagsausgabe §
DOI: 10.5445/IR/1000125907
Veröffentlicht am 10.11.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 0303-6898, 1467-9469
KITopen-ID: 1000125907
Erschienen in Scandinavian journal of statistics
Seiten sjos.12477
Vorab online veröffentlicht am 17.09.2020
Nachgewiesen in Scopus
Web of Science
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