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High-dimensional test for normality

Jérémie Kellner 1, 2 Alain Celisse 2
1 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
2 LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability to a wider range of data. Theoretical results are derived for the Type-I and Type-II errors. They guarantee the control of Type-I error at prescribed level and an exponentially fast decrease of the Type-II error. Synthetic and real data also illustrate the practical improvement allowed by our test compared with other leading approaches in high-dimensional settings.
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Conference papers
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https://hal.inria.fr/hal-01091513
Contributor : Jérémie Kellner <>
Submitted on : Friday, December 5, 2014 - 3:19:46 PM
Last modification on : Friday, November 27, 2020 - 2:18:02 PM

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  • HAL Id : hal-01091513, version 1

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CNRS | INRIA | INSMI | UNIV-LILLE

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Jérémie Kellner, Alain Celisse. High-dimensional test for normality. Journées des Statistiques, Jun 2014, Rennes, France. ⟨hal-01091513⟩

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