Open Access
Translator Disclaimer
December 2005 Sharp adaptive estimation of the drift function for ergodic diffusions
Arnak Dalalyan
Ann. Statist. 33(6): 2507-2528 (December 2005). DOI: 10.1214/009053605000000615


The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift S(⋅) is supposed to belong to a nonparametric class of smooth functions of order k≥1, but the value of k is not known to the statistician. A fully data-driven procedure of estimating the drift function is proposed, using the estimated risk minimization method. The sharp adaptivity of this procedure is proven up to an optimal constant, when the quality of the estimation is measured by the integrated squared error weighted by the square of the invariant density.


Download Citation

Arnak Dalalyan. "Sharp adaptive estimation of the drift function for ergodic diffusions." Ann. Statist. 33 (6) 2507 - 2528, December 2005.


Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1084.62079
MathSciNet: MR2253093
Digital Object Identifier: 10.1214/009053605000000615

Primary: 62G07 , 62G20 , 62M05

Keywords: Ergodic diffusion , invariant density , minimax drift estimation , Pinsker’s constant , sharp adaptivity

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 6 • December 2005
Back to Top