Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case

Arnak S. Dalalyan (1) , Markus Reiss (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]

Asymptotic local equivalence in the sense of Le Cam is established for inference on the drift in multidimensional ergodic diffusions and an accompanying sequence of Gaussian shift experiments. The nonparametric local neighbourhoods can be attained for any dimension, provided the regularity of the drift is sufficiently large. In addition, a heteroskedastic Gaussian regression experiment is given, which is also locally asymptotically equivalent and which does not depend on the centre of localisation. For one direction of the equivalence an explicit Markov kernel is constructed.

Mots clés: Asymptotic equivalence; statistical experiment; Le Cam distance; ergodic diffusion; Gaussian shift; heteroskedastic regression

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Arnak S. Dalalyan, Markus Reiss. Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case. Probability Theory and Related Fields, 2007, 137 (1-2), pp.25-47. ⟨hal-00004828v2⟩