On guaranteed parameter estimation of a multiparameter linear regression process

Abstract

This paper presents a sequential estimation procedure for the unknown parameters of a continuous-time stochastic linear regression process. As an example, 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 L q -norm for fixed q ≥ 2 . The proposed procedure works in the mentioned examples for all possible values of unknown dynamic parameters on the plane R 2 for the autoregressive processes and on the plane R 2 with the exception of some lines for the linear stochastic delay equations. The asymptotic behaviour 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.