New normality test in high dimension with kernel methods

Jérémie Kellner (1, 2) , Alain Celisse (1, 2)

1 MODAL - MOdel for Data Analysis and Learning
2 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Mots clés: kernel; normality test; rkhs; reproducing kernel Hilbert space; Hilbert space embeddings; characteristic kernel

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jérémie Kellner, Alain Celisse. New normality test in high dimension with kernel methods. 2014. ⟨hal-00977839⟩