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May, 1981 Asymptotic Theory of Nonlinear Least Squares Estimation
Chien-Fu Wu
Ann. Statist. 9(3): 501-513 (May, 1981). DOI: 10.1214/aos/1176345455

Abstract

For a linear regression model, the necessary and sufficient condition for the asymptotic consistency of the least squares estimator is known. An analogous condition for the nonlinear model is considered in this paper. The condition is proved to be necessary for the existence of any weakly consistent estimator, including the least squares estimator. It is also sufficient for the strong consistency of the nonlinear least squares estimator if the parameter space is finite. For an arbitrary compact parameter space, its sufficiency for strong consistency is proved under additional conditions in a sense weaker than previously assumed. The proof involves a novel use of the strong law of large numbers in $C(S)$. Asymptotic normality is also established.

Citation

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Chien-Fu Wu. "Asymptotic Theory of Nonlinear Least Squares Estimation." Ann. Statist. 9 (3) 501 - 513, May, 1981. https://doi.org/10.1214/aos/1176345455

Information

Published: May, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0475.62050
MathSciNet: MR615427
Digital Object Identifier: 10.1214/aos/1176345455

Subjects:
Primary: 62J02
Secondary: 62F12

Keywords: asymptotic normality , Nonlinear least squares estimator , nonlinear model , strong law of large numbers in $C(S)$ , weak and strong consistency

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 3 • May, 1981
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