Open Access
November 2015 Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions
L.I. Galtchouk, S.M. Pergamenshchikov
Bernoulli 21(4): 2569-2594 (November 2015). DOI: 10.3150/14-BEJ655


A truncated sequential procedure is constructed for estimating the drift coefficient at a given state point based on discrete data of ergodic diffusion process. A nonasymptotic upper bound is obtained for a pointwise absolute error risk. The optimal convergence rate and a sharp constant in the bounds are found for the asymptotic pointwise minimax risk. As a consequence, the efficiency is obtained of the proposed sequential procedure.


Download Citation

L.I. Galtchouk. S.M. Pergamenshchikov. "Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions." Bernoulli 21 (4) 2569 - 2594, November 2015.


Received: 1 March 2012; Revised: 1 December 2012; Published: November 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1342.60132
MathSciNet: MR3378478
Digital Object Identifier: 10.3150/14-BEJ655

Keywords: discrete data , drift coefficient estimation , efficient procedure , ergodic diffusion process , minimax , nonparametric sequential estimation

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 4 • November 2015
Back to Top