Hermite ranks and -statistics

Céline Levy Leduc (1) , M. S. Taqqu (2)

1 MIA-Paris - Mathématiques et Informatique Appliquées
2 Department of Mathematics

We focus on the asymptotic behavior of U-statistics of the type Sigma(1 <= i not equal j <= n) h(X-i, X-j) in the long-range dependence setting, where (X-i)(i >= 1) is a stationary mean-zero Gaussian process. Since (X-i)(i >= 1) is Gaussian, can be decomposed in Hermite polynomials. The goal of this paper is to compare the different notions of Hermite rank and to provide conditions for the remainder term in the decomposition to be asymptotically negligeable.

Mots clés: Hermite polynomials; U-statistics; long-range dependence

Domaines: Statistiques [math.ST]

Céline Levy Leduc, M. S. Taqqu. Hermite ranks and -statistics. Metrika, 2014, 77 (1), pp.105 - 136. ⟨10.1007/s00184-013-0474-4⟩. ⟨hal-01197638⟩