Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case

Abstract

Abstract. 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.

Nonparametric trend coefficient estimation for multidimensional diffusions

“…Results close to those presented in this section were independently obtained in [6]. However, the approach of this Note may be of interest, since the estimators employed and the methods used in the proofs are different.…”

Conditions minimales de consistance pour la sélection de variables en grande dimension

“…La (presque) minimalité de ces conditions a été également prouvée. Dans l'avenir, nous voudrions étendre ces résultats aux modèles de diffusions, en utilisant les techniques de [4], ce qui permettrait de réduire la dimension et d'utiliser des méthodes d'adaptations clasiques [2]. Il serait également intéressant de mener une étude analogue pour les modèles à plusieurs directions révélatrices [3].…”

Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments

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