Spectral estimation for diffusions with random sampling times
Statistics Theory
2017-10-12 v3 Probability
Methodology
Statistics Theory
Abstract
The nonparametric estimation of the volatility and the drift coefficient of a scalar diffusion is studied when the process is observed at random time points. The constructed estimator generalizes the spectral method by Gobet, Hoffmann and Rei{\ss} [Ann. Statist. 32 (2006), 2223-2253]. The estimation procedure is optimal in the minimax sense and adaptive with respect to the sampling time distribution and the regularity of the coefficients. The proofs are based on the eigenvalue problem for the generalized transition operator. The finite sample performance is illustrated in a numerical example.
Cite
@article{arxiv.1503.00466,
title = {Spectral estimation for diffusions with random sampling times},
author = {Jakub Chorowski and Mathias Trabs},
journal= {arXiv preprint arXiv:1503.00466},
year = {2017}
}
Comments
30 pages, 2 figures