Penalized nonparametric mean square estimation of the coefficients of diffusion processes

Details Penalized nonparametric mean square estimation of the coefficients of diffusion processes Penalized nonparametric mean square estimation of the coefficients of diffusion processes

2007-08-30

arxiv.org/abs/0708.4165v1

Bernoulli 2007, Vol. 13, No. 2, 514-543

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.3150/07-BEJ5173 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ5173

We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and diffusion coefficients obtained by a penalized least squares approach. Our estimators belong to a finite-dimensional function space whose dimension is selected by a data-driven method. We provide non-asymptotic risk bounds for the estimators. When the sampling interval tends to zero while the number of observations and the length of the observation time interval tend to infinity, we show that our estimators reach the minimax optimal rates of convergence. Numerical results based on exact simulations of diffusion processes are given for several examples of models and illustrate the qualities of our estimation algorithms.

Affiliated with

Also associated with

No associations

Rating

Penalized nonparametric mean square estimation of the coefficients of diffusion processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Penalized nonparametric mean square estimation of the coefficients of diffusion processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Penalized nonparametric mean square estimation of the coefficients of diffusion processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-206089