Adaptive nonparametric drift estimation for diffusion processes using Faber–Schauder expansions
Artikel i vetenskaplig tidskrift, 2018

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 L2-norm that are optimal up to a log factor. Contraction rates in Lp-norms with p∈ (2 , ∞] are derived as well.

Författare

Frank van der Meulen

TU Delft

Moritz Schauer

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Jan van Waaij

Universiteit Van Amsterdam

Statistical Inference for Stochastic Processes

1387-0874 (ISSN) 15729311 (eISSN)

Vol. 21 3 603-628

Ämneskategorier (SSIF 2025)

Sannolikhetsteori och statistik

DOI

10.1007/s11203-017-9163-7

Mer information

Senast uppdaterat

2025-07-01