Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case |
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Authors: | Arnak Dalalyan Markus Reiß |
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Affiliation: | (1) Laboratoire de Probabilités, Université Paris VI, Place Jussieu, 75252 Paris Cedex 05, France;(2) Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany |
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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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Keywords: | 62B15 62G05 62G07 62G20 62M05 |
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