Nonparametric estimation of scalar diffusions based on low frequency data
| dc.creator | Gobet, Emmanuel | |
| dc.creator | Hoffmann, Marc | |
| dc.creator | Reiss, Markus | |
| dc.date | 2005-03-29 | |
| dc.date.accessioned | 2026-07-07T08:06:47Z | |
| dc.date.available | 2026-07-07T08:06:47Z | |
| dc.description | We study the problem of estimating the coefficients of a diffusion (X_t,t\geq 0); the estimation is based on discrete data X_{nΔ},n=0,1,...,N. The sampling frequency Δ^{-1} is constant, and asymptotics are taken as the number N of observations tends to infinity. We prove that the problem of estimating both the diffusion coefficient (the volatility) and the drift in a nonparametric setting is ill-posed: the minimax rates of convergence for Sobolev constraints and squared-error loss coincide with that of a, respectively, first- and second-order linear inverse problem. To ensure ergodicity and limit technical difficulties we restrict ourselves to scalar diffusions living on a compact interval with reflecting boundary conditions. Our approach is based on the spectral analysis of the associated Markov semigroup. A rate-optimal estimation of the coefficients is obtained via the nonparametric estimation of an eigenvalue-eigenfunction pair of the transition operator of the discrete time Markov chain (X_{nΔ},n=0,1,...,N) in a suitable Sobolev norm, together with an estimation of its invariant density. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053604000000797 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0503680 | |
| dc.identifier | http://arxiv.org/abs/math/0503680 | |
| dc.identifier | Annals of Statistics 2004, Vol. 32, No. 5, 2223-2253 | |
| dc.identifier | doi:10.1214/009053604000000797 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130728 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G99, 62M05, 62M15 (Primary) | |
| dc.title | Nonparametric estimation of scalar diffusions based on low frequency data | |
| dc.type | text |