A One-Sample Test for Normality with Kernel Methods

Jérémie Kellner 1, 2 Alain Celisse 2, 1
1 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, CERIM - Santé publique : épidémiologie et qualité des soins-EA 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test data for normality or to test parameters (mean and covariance) if data are assumed Gaussian. Our test is based on the same principle as the MMD (Maximum Mean Discrepancy) which is usually used for two-sample tests such as homogeneity or independence testing. Our method makes use of a special kind of parametric bootstrap (typical of goodness-of-fit tests) which is computationally more efficient than standard parametric bootstrap. Moreover, an upper bound for the Type-II error highlights the dependence on influential quantities. Experiments illustrate the practical improvement allowed by our test in high-dimensional settings where common normality tests are known to fail. We also consider an application to covariance rank selection through a sequential procedure.
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https://hal.archives-ouvertes.fr/hal-01175237
Contributor : Jérémie Kellner <>
Submitted on : Friday, July 10, 2015 - 2:03:34 PM
Last modification on : Thursday, February 21, 2019 - 10:34:08 AM
Long-term archiving on: Monday, October 12, 2015 - 11:31:56 AM

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  • HAL Id : hal-01175237, version 1
  • ARXIV : 1507.02904

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Jérémie Kellner, Alain Celisse. A One-Sample Test for Normality with Kernel Methods. 2015. ⟨hal-01175237⟩

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