Global smoothness estimation of a Gaussian process from general sequence designs.

Delphine Blanke (1) , Céline Vial (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 IP - Institut Pascal

We consider a real Gaussian process X with global unknown smoothness (r0, β0): more precisely X (r 0) , r0 ∈ N 0 , is supposed to be locally stationary with Hölder exponent β0, β0 ∈]0, 1[. For X observed at a finite set of points, we derive estimators of r0 and β0 based on the quadratic variations for the divided differences of X. Under mild conditions, we obtain an exponential bound for estimating r0, as well as sharp rates of convergence (up to logarithmic factors) for the estimation of β0. An extensive simulation study illustrates the finite-sample properties of both estimators for different types of processes and we also include two real data applications.

Mots clés: Inference for Gaussian processes; locally stationary process; divided differences; quadratic variations; unevenly spaced data

Domaines: Mathématiques [math]

Delphine Blanke, Céline Vial. Global smoothness estimation of a Gaussian process from general sequence designs.. Electronic Journal of Statistics , 2014, 8 (1), pp.1152-1187. ⟨10.1214/14-EJS925⟩. ⟨hal-01325853⟩