| Type de publication : |
 |
Preprint, Working Paper, Document sans référence, etc. |
|
| Domaine : |
|
|
|
| Titre : |
|
Asymptotic properties of U-processes under long-range dependence |
|
| Auteur(s) : |
|
Céline Lévy-Leduc ( ) 1, Hélène Boistard 2, Eric Moulines 1, Murad S. Taqqu 3, Valderio A. Reisen 4 |
|
| Laboratoire : |
|
|
|
| Résumé : |
|
Let $(X_i)_{i\geq 1}$ be a stationary mean-zero Gaussian process with covariances $\rho(k)=\PE(X_{1}X_{k+1})$ satisfying: $\rho(0)=1$ and $\rho(k)=k^{-D} L(k)$ where $D$ is in $(0,1)$ and $L$ is slowly varying at infinity. Consider the $U$-process $\{U_n(r),\; r\in I\}$ defined as $$ U_n(r)=\frac{1}{n(n-1)}\sum_{1\leq i\neq j\leq n}\1_{\{G(X_i,X_j)\leq r\}}\; , $$ where $I$ is an interval included in $\rset$ and $G$ is a symmetric function. In this paper, we provide central and non-central limit theorems for $U_n$. They are used to derive the asymptotic behavior of the Hodges-Lehmann estimator, the Wilcoxon-signed rank statistic, the sample correlation integral and an associated scale estimator. The limiting distributions are expressed through multiple Wiener-Itô integrals. |
|
Langue du texte
intégral : |
|
Anglais |
|
Date de production,
écriture : |
|
23/12/2009 |
|
|
| Mots Clés : |
|
Long-range dependence – $U$-process – Hodges-Lehmann estimator – Wilcoxon-signed rank test – sample correlation integral |
|
|
Récupérer au format
