Adaptive nonparametric drift estimation for diffusion processes using Faber–Schauder expansions

Adaptive nonparametric drift estimation for diffusion processes using Faber–Schauder expansions

van der Meulen, F.H. (TU Delft Statistics)
Schauer, M.R. (Universiteit Leiden)
van Waaij, Jan (Universiteit van Amsterdam)

2017

We consider the problem of nonparametric estimation of the drift of a continuously observed one-dimensional diffusion with periodic drift. Motivated by computational considerations, van der Meulen et al. (Comput Stat Data Anal 71:615–632, 2014) defined a prior on the drift as a randomly truncated and randomly scaled Faber–Schauder series expansion with Gaussian coefficients. We study the behaviour of the posterior obtained from this prior from a frequentist asymptotic point of view. If the true data generating drift is smooth, it is proved that the posterior is adaptive with posterior contraction rates for the (Formula presented.)-norm that are optimal up to a log factor. Contraction rates in (Formula presented.)-norms with (Formula presented.) are derived as well.

http://resolver.tudelft.nl/uuid:4d38afd4-dd71-4042-89ee-0809669ef8ea

https://doi.org/10.1007/s11203-017-9163-7

1387-0874

Statistical Inference for Stochastic Processes, 1-26

Institutional Repository

journal article

© 2017 F.H. van der Meulen, M.R. Schauer, Jan van Waaij