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Nonlinear least-squares estimation. (English) Zbl 1085.62027
Summary: The paper uses empirical process techniques to study the asymptotics of the least-squares estimators (LSE) for fitting of nonlinear regression functions. By combining and extending ideas of C.-F. Wu [Ann. Stat. 9, 501–513 (1981; Zbl 0475.62050)] and S. van de Geer [ibid. 18, No. 2, 907–924 (1990; Zbl 0709.62040)], it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu illustrates the use of the new theorems, leading to a normal approximation to the LSE with unusual logarithmic rescalings.

62F12 Asymptotic properties of parametric estimators
62J02 General nonlinear regression
60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62M99 Inference from stochastic processes
Full Text: DOI
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