Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case - Archive ouverte HAL Access content directly
Journal Articles Probability Theory and Related Fields Year : 2007

Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case

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.
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Dates and versions

hal-00004828 , version 1 (03-05-2005)
hal-00004828 , version 2 (06-05-2005)

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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⟩
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