International Journal of Statistics and Management Systems, 2007, Vol. 2, No. 1–2, pp. 1–21.
c 2007 Serials Publications
On a Berry–Esseen type bound for the least
squares estimator for diffusion processes
based on discrete observations
M. N. Mishra† and B. L. S. Prakasa Rao
∗
‡
Abstract
This paper is concerned with the distribution of a least squares estimator of the
drift parameter in a stochastic differential equation with small diffusion observed
over discrete set of time points with high frequency. The rate of convergence of the
distribution of the least squares estimator to the standard normal distribution with
an error bound is obtained when both the discretization step and the noise intensity
decrease to zero.
∗
Received: March 10, 2006; Accepted: November 24, 2006.
Key words and phrases: Diffusion processes, Berry–Esseen bound.
AMS 2000 subject classifications. Primary 60J60; secondary 60H10.
†
Mailing Address: Institute of Mathematics and Applications, Bhubaneswar 751013, India. E–mail:
mnmeeshraw@yahoo.com.
‡
Mailing Address: Department of Mathematics and Statistics, University of Hyderabad, Hyderabad
500046, India. E–mail: blsprsm@uohyd.ernet.in.