Convergence of quadratic forms for random fields and its application to the convergence of empirical covariances - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2008

Convergence of quadratic forms for random fields and its application to the convergence of empirical covariances

Anne Philippe

Abstract

Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. Similarly to the one dimensional case, we prove that the quadratic forms, appropriately normalized, may have Gaussian or non-Gaussian limits. However the dichotomy observed in $d=1$ cannot be stated so easily, due to the possible occurrence of anisotropic strong dependence in $d>1$. We apply our theorems to obtain the asymptotic behavior of the empirical covariances, which is a particular example of quadratic forms.
Fichier principal
Vignette du fichier
Lavancier_Philippe2008.pdf (243.87 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00348833 , version 1 (22-12-2008)
hal-00348833 , version 2 (08-10-2009)
hal-00348833 , version 3 (07-01-2010)

Identifiers

Cite

Frédéric Lavancier, Anne Philippe. Convergence of quadratic forms for random fields and its application to the convergence of empirical covariances. 2008. ⟨hal-00348833v1⟩

Collections

FMPL
100 View
406 Download

Altmetric

Share

Gmail Facebook X LinkedIn More