Open Access
Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

Claudia Strauch. "Adaptive invariant density estimation for ergodic diffusions over anisotropic classes." Ann. Statist. 46 (6B) 3451 - 3480, December 2018. https://doi.org/10.1214/17-AOS1664

Information

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

Subjects:
Primary: 62G07 , 62G20 , 62M05

Keywords: Adaptation , Anisotropic density estimation , Ergodic diffusion

Rights: Copyright © 2018 Institute of Mathematical Statistics

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.46 • No. 6B • December 2018
Back to Top