Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case
By Arnak S. Dalalyan, Markus Reiß. 2005
81 citations recorded by the source corpus.
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.
Subfields: Radiology, Nuclear Medicine and Imaging, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/0cb104c1106cea3613ae4a9b93a82d0e9a7986e2
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In Radiology, Nuclear Medicine and Imaging
In Statistics and Probability
- Kolyan Ray
- Richard Nickl
- Markus Reiß
- Judith Rousseau
- I. Castillo
- Evarist Gin'e
- Botond Szab'o
- D. Chetverikov
Citations in the corpus
- Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions (2018, methodology): “In the measurement model we consider here, convergence rates of certain multivariate nonparametric kernel-type estimators were first obtained in Dalalyan and Reiß [16], and further recent results in this direction are by Strauch [45, 46, 47], who obtained sharp (and adaptive) convergence rate result”
- Asymptotic equivalence for nonparametric regression with multivariate and random design (2006, methodology): “For the dynamic model of ergodic diffusions Dalalyan and Reiß (2006) have established multidimensional asymptotic equivalence with a white noise model.”