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Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case

By Arnak S. Dalalyan and Markus Reiss

Abstract

03 May 2005, 23 pagesInternational audienceAsymptotic 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

Topics: statistical experiment, Le Cam distance, Asymptotic equivalence, Gaussian shift, heteroskedastic regression, ergodic diffusion, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Publisher: Springer Verlag
Year: 2007
OAI identifier: oai:HAL:hal-00004828v2
Provided by: Hal-Diderot
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