TY - JOUR
T1 - Adaptive nonparametric drift estimation for diffusion processes using Faber–Schauder expansions
AU - van der Meulen, Frank
AU - Schauer, Moritz
AU - van Waaij, Jan
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85021147048&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:4d38afd4-dd71-4042-89ee-0809669ef8ea
U2 - 10.1007/s11203-017-9163-7
DO - 10.1007/s11203-017-9163-7
M3 - Article
AN - SCOPUS:85021147048
SN - 1387-0874
SP - 1
EP - 26
JO - Statistical Inference for Stochastic Processes
JF - Statistical Inference for Stochastic Processes
ER -