On guaranteed parameter estimation of a multiparameter linear regression process

Uwe Küchler , Vyacheslav A. Vasiliev

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 7/2009, 60 pp.

MSC 2000

34K50 Stochastic delay equations

60H10 Stochastic ordinary differential equations

ZDM: 62L10

CR: 62L12

Abstract
This paper presents a sequential estimation procedure for the unknown parameters of a continuous-time stochastic linear regression process. As examples the sequential estimation problem of two dynamic parameters in stochastic linear systems with memory and in autoregressive processes is solved. The estimation procedure is based on the least squares method with weights and yields estimators with guaranteed accuracy in the sense of the Lq-norm for fixed q > 2. The proposed procedure works in the mentioned examples for all possible values of unknown dynamic parameters on the plane R2 for the autoregressive processes and on the plane R2 with the exception of some lines for the linear stochastic delay equations. The asymptotic behavior of the duration of observations is determined. The general estimation procedure is designed for two- or more-parametric models. It is shown, that the proposed procedure can be applied to the sequential parameter estimation problem of affine stochastic delay differential equations and autoregressive processes of an arbitrary order.