Adaptive wavelet-based estimator of the memory parameter for stationary Gaussian processes

被引：7

作者：

Bardet, Jean-Marc ^{[1
]}

Bibi, Hatem ^{[1
]}

Jouini, Abdellatif ^{[2
]}

机构：

[1] Univ Paris 01, Samos Matisse CES, CNRS, UMR 8174, F-75013 Paris, France

[2] Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia

来源：

BERNOULLI | 2008年 / 14卷 / 03期

关键词：

wavelet analysis; long range dependence; memory parameter; semi-parametric estimation; adaptive estimation;

D O I：

10.3150/07-BEJ6151

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This work is intended as a contribution to the theory of a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular, we introduce and develop the choice of a data-driven optimal bandwidth. Moreover, we establish a central limit theorem for the estimator of the memory parameter with the minimax rate of convergence (Lip to a logarithm factor). The quality of the estimators is demonstrated via simulations.

引用

页码：691 / 724

页数：34

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