Statistics and Data Science Seminar
Milan Stehlik
Johannes Kepler University, Austria and University of Valparaiso, Chile
Recent advances in optimal design for correlated Processes
Abstract: Since 2004 there were many results obtained regarding the determination of optimal designs for models with
correlated errors. This task is substantially more difficult than in case of iid errors and for this reason
not so well developed. Stochastic process with parametrized mean and covariance is observed over a compact
set. The information obtained from observations is measured through the information functional (defined on
the Fisher information matrix). The role of equidistant designs has been recognized; e.g. such designs have
been proved to be optimal for parameter of trend of stationary Ornstein-Uhlenbeck process, also for
nonstationary Ornstein-Uhlenbeck process, both for prediction and estimation. We can conclude that if
only trend parameters are of interest, the designs covering more-less uniformly the whole design space
are rather efficient when correlation decreases exponentially. This concept is also valid for so called
monotonic set designs. We will concentrate on several important issues regarding regularity conditions for
quality of ``plug-in" approach from iid case. Namely, 1) relaxing the continuity of covariance. We will
introduce the regularity conditions for isotropic processes with semicontinuous covariance such that
increasing domain asymptotic is still feasible, however more flexible behavior may occur here.
In particular, the role of the nugget effect will be illustrated. 2) regarding quality of
approximation of inverse information matrix by variance-covariance, Pazman (2007) discusses
theoretical background and formulated important conditions, which are fundamental.
Zhu and Stein (2005) made simulations experiments. Finally, application in troposphere
methane modelling will be illustrating the developed methods.
Wednesday October 19, 2016 at 4:00 PM in SEO 636