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Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case
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  • Published: 24 April 2006

Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case

  • Arnak Dalalyan1 &
  • Markus Reiß2 

Probability Theory and Related Fields volume 137, pages 25–47 (2007)Cite this article

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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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Authors and Affiliations

  1. Laboratoire de Probabilités, Université Paris VI, Place Jussieu, 75252, Paris Cedex 05, France

    Arnak Dalalyan

  2. Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Markus Reiß

Authors
  1. Arnak Dalalyan
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  2. Markus Reiß
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Correspondence to Arnak Dalalyan.

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Dalalyan, A., Reiß, M. Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case. Probab. Theory Relat. Fields 137, 25–47 (2007). https://doi.org/10.1007/s00440-006-0502-7

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  • Received: 06 May 2005

  • Revised: 30 January 2006

  • Published: 24 April 2006

  • Issue Date: January 2007

  • DOI: https://doi.org/10.1007/s00440-006-0502-7

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Mathematics Subject Classification (2000)

  • 62B15
  • 62G05
  • 62G07
  • 62G20
  • 62M05

Keywords or phrases

  • Asymptotic equivalence
  • Statistical experiment
  • Le Cam distance
  • Ergodic diffusion
  • Gaussian shift
  • Heteroskedastic regression
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