The Annals of Statistics

Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems

Tze Leung Lai and Ching Zong Wei

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Abstract

Strong consistency and asymptotic normality of least squares estimates in stochastic regression models are established under certain weak assumptions on the stochastic regressors and errors. We discuss applications of these results to interval estimation of the regression parameters and to recursive on-line identification and control schemes for linear dynamic systems.

Article information

Source
Ann. Statist. Volume 10, Number 1 (1982), 154-166.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176345697

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176345697

Mathematical Reviews number (MathSciNet)
MR642726

Zentralblatt MATH identifier
0649.62060

Subjects
Primary: 62J05: Linear regression
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60F15: Strong theorems 60G45 93B30: System identification 93C40: Adaptive control

Keywords
Stochastic regressors least squares system identification adaptive control dynamic models strong consistency asymptotic normality martingales

Citation

Lai, Tze Leung; Wei, Ching Zong. Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems. The Annals of Statistics 10 (1982), no. 1, 154--166. doi:10.1214/aos/1176345697. http://projecteuclid.org/euclid.aos/1176345697.


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