Identification of Semi-Linear Models within an Errors-In-Variables Framework

Rik Pintelon () and Johan Schoukens ()
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Rik Pintelon: Vrije Universiteit Brussel, department ELEC
Johan Schoukens: Vrije Universiteit Brussel, department ELEC

A chapter in Total Least Squares and Errors-in-Variables Modeling, 2002, pp 165-177 from Springer

Abstract: Abstract Semi-linear models are models which are linear-in-the-observations and (non)linear in the model parameters. Assuming that all observations are noisy (errors-in-variables framework), the Cramér-Rao lower bound of the model parameters is calculated, and the stochastic properties (strong convergence, convergence rate, strong consistency, asymptotic normality, asymptotic efficiency) of the Markov estimator are analyzed. It follows that in general the Markov estimator is strongly consistent, and asymptotically inefficient (in case of Gaussian errors the estimator does not reach the Cramér-Rao lower bound). Sufficient conditions for the asymptotic efficiency of the Markov estimator are given. The theory is applicable to, for example, signal modelling and multivariable system identification, both in time and frequency domains.

Keywords: Markov estimator; system identification; signal processing; semi-linear errors-in-variables model; estimating function. (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-3552-0_15

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DOI: 10.1007/978-94-017-3552-0_15

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