Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. (English) Zbl 0649.62060

Lai, Tze Leung; Wei, Ching Zong

Ann. Stat. 10, 154-166 (1982).

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.

MSC:

62J05	Linear regression; mixed models
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
93E12	Identification in stochastic control theory
93B30	System identification
93C40	Adaptive control/observation systems
60F15	Strong limit theorems

Keywords:

adaptive control; martingales; Strong consistency; asymptotic normality; least squares estimates; stochastic regression models; interval estimation; recursive on-line identification; linear dynamic systems