Work

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

Year: 2017

Type: article

Abstract: 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 $$L_2$$ -norm that are optimal up to a log factor. Contraction rates in $$L_p$$ -norms with $$p\in (2,\infty ]$$ are derived as well.

Source: Statistical Inference for Stochastic Processes

DOI: 10.1007/s11203-017-9163-7

Authors: Frank van der Meulen, Moritz Schauer, Jan van Waaij

Institutions: Delft University of Technology, Leiden University, University of Amsterdam

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Universiteit van Amsterdam, Nederlandse Organisatie voor Wetenschappelijk Onderzoek