On estimation of regularity for Gaussian processes

Delphine Blanke (1) , Céline Vial (2)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie
2 ICJ - Institut Camille Jordan

We consider a real Gaussian process $X$ with unknown smoothness $r_0$ where $r_0$ is a nonnegative integer and the mean-square derivative $X^{(r_0)}$ is supposed to be locally stationary of index $\beta_0$. From $n+1$ equidistant observations, we propose and study an estimator of $(r_0,\beta_0)$ based on results for quadratic variations of the underlying process. Various numerical studies of these estimators derive their properties for finite sample size and different types of processes, and are also completed by two examples of application to real data.

Mots clés: Inference for Gaussian processes; Locally stationary process; Quadratic variations

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Delphine Blanke, Céline Vial. On estimation of regularity for Gaussian processes. 2012. ⟨hal-00750409v1⟩