Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions
Statistics Theory
2015-09-21 v3 Statistics Theory
Abstract
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.
Cite
@article{arxiv.1411.0515,
title = {Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions},
author = {L. I. Galtchouk and S. M. Pergamenshchikov},
journal= {arXiv preprint arXiv:1411.0515},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.3150/14-BEJ655 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)