Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments - Institut de Mathématiques de Toulouse Accéder directement au contenu
Article Dans Une Revue ESAIM: Probability and Statistics Année : 2020

Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments

Résumé

We consider the semi-parametric estimation of the scale parameter of the variogram of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based both on quadratic variations and the moment method. We provide asymptotic approximations of the mean and variance of this estimator, together with asymptotic normality results, for a large class of Gaussian processes. We allow for general mean functions, provide minimax upper bounds and study the aggregation of several estimators based on various variation sequences. In extensive simulation studies, we show that the asymptotic results accurately depict the finite-sample situations already for small to moderate sample sizes. We also compare various variation sequences and highlight the efficiency of the aggregation procedure.
Fichier principal
Vignette du fichier
ps190095.pdf (1.1 Mo) Télécharger le fichier
Origine : Publication financée par une institution

Dates et versions

hal-03022877 , version 1 (25-11-2020)

Identifiants

Citer

Jean-Marc Azaïs, François Bachoc, Agnès Lagnoux, Thi Mong Ngoc Nguyen. Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments. ESAIM: Probability and Statistics, 2020, 24, pp.842-882. ⟨10.1051/ps/2020021⟩. ⟨hal-03022877⟩
29 Consultations
68 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More