Title: D-optimal designs for complex Ornstein-Uhlenbeck processes,
Abstract: Complex Ornstein-Uhlenbeck (OU) processes have various applications in
statistical modelling. They play role e.g. in the description of the motion of
a charged test particle in a constant magnetic field or in the study of
rotating waves in time-dependent reaction diffusion systems, whereas Kolmogorov
used such a process to model the so-called Chandler wobble, small deviation in
the Earth's axis of rotation. In these applications parameter estimation and
model fitting is based on discrete observations of the underlying stochastic
process, however, the accuracy of the results strongly depend on the
observation points.
This paper studies the properties of D-optimal designs for estimating the
parameters of a complex OU process with a trend. We show that in contrast with
the case of the classical real OU process, a D-optimal design exists not only
for the trend parameter, but also for joint estimation of the covariance
parameters, moreover, these optimal designs are equidistant.