Open Access
December 2018 Adaptive invariant density estimation for ergodic diffusions over anisotropic classes
Claudia Strauch
Ann. Statist. 46(6B): 3451-3480 (December 2018). DOI: 10.1214/17-AOS1664


Consider some multivariate diffusion process $\mathbf{X}=(X_{t})_{t\geq0}$ with unique invariant probability measure and associated invariant density $\rho$, and assume that a continuous record of observations $X^{T}=(X_{t})_{0\leq t\leq T}$ of $\mathbf{X}$ is available. Recent results on functional inequalities for symmetric Markov semigroups are used in the statistical analysis of kernel estimators $\widehat{\rho}_{T}=\widehat{\rho}_{T}(X^{T})$ of $\rho$. For the basic problem of estimation with respect to $\mathrm{sup}$-norm risk under anisotropic Hölder smoothness constraints, the proposed approach yields an adaptive estimator which converges at a substantially faster rate than in standard multivariate density estimation from i.i.d. observations.


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Claudia Strauch. "Adaptive invariant density estimation for ergodic diffusions over anisotropic classes." Ann. Statist. 46 (6B) 3451 - 3480, December 2018.


Received: 1 March 2017; Revised: 1 October 2017; Published: December 2018
First available in Project Euclid: 11 September 2018

zbMATH: 06965694
MathSciNet: MR3852658
Digital Object Identifier: 10.1214/17-AOS1664

Primary: 62G07 , 62G20 , 62M05

Keywords: Adaptation , Anisotropic density estimation , Ergodic diffusion

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 6B • December 2018
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