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The theory of functional least squares

Part of: Linear inference, regression Limit theorems

Published online by Cambridge University Press:  09 April 2009

Sándor Csörgő
Sándor Csörgő
Affiliation:
Bolyai Institute Szeged UniversityH-6720 Szeged Hungary
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Abstract

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The functional least squares procedure of Chambers and Heathcote for estimating the slope parameter in a linear regression model is analysed. Strong uniform consistency for the family of these estimators is proved together with a necessary and sufficient condition for weak convergence in the space of continuous vector valued functions. These results are then used to develop the asymptotic normality of an adaptive version of the functional least squares estimator with minimum limiting variance.

MSC classification

Secondary: 62J05: Linear regression 60F17: Functional limit theorems; invariance principles
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 3 , June 1983 , pp. 336 - 355
Copyright
Copyright © Australian Mathematical Society 1983

References

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