Dynamic realizations of sufficient sequences

Author

Dickinson, Bradley W. ; Sontag, Eduardo D.

Volume

31

Issue

5

fYear

1985

fDate

9/1/1985 12:00:00 AM

Firstpage

670

Lastpage

676

Abstract

Let $(U_{1},U_{2}, \\cdots )$ be a sequence of observed random variables and $(T_{1}(U_{1}),T_{2}(U_{1}, U_{2}), \\cdots )$ be a corresponding sequence of sufficient statistics (a sufficient sequence). Under certain regularity conditions, the sufficient sequence defines the input/output map of a time-varying, discrete-time nonlinear system. This system provides a recursive way of updating the sufficient statistic as new observations are made. Conditions are provided assuring that such a system evolves in a state space of minimal dimension. Several examples are provided to illustrate how this notion of dimensional minimality is related to other properties of sufficient sequences. The results can be used to verify the form of the minimum dimension (discrete-time) nonlinear filter associated with the autoregressive parameter estimation problem.

Keywords

Autoregressive processes; Nonlinear systems; Sequences; Nonlinear filters; Nonlinear systems; Parameter estimation; Random variables; Signal analysis; Signal processing; State-space methods; Statistics; Time series analysis; Time varying systems;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1985.1057092

Filename

1057092