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Nonlinear least-squares estimation

Author

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  • Pollard, David
  • Radchenko, Peter

Abstract

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator (LSE) for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, 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's illustrates the use of the new theorems, leading to a normal approximation to the LSE with unusual logarithmic rescalings.

Suggested Citation

  • Pollard, David & Radchenko, Peter, 2006. "Nonlinear least-squares estimation," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 548-562, February.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:548-562
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    Citations

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    Cited by:

    1. Radchenko, Peter, 2015. "High dimensional single index models," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 266-282.
    2. Pengfei Liu & Mengchen Zhang & Ru Zhang & Qin Zhou, 2021. "Robust Estimation and Tests for Parameters of Some Nonlinear Regression Models," Mathematics, MDPI, vol. 9(6), pages 1-16, March.
    3. Cheng Maolin & Shi Guojun & Han Yun, 2019. "A Modified CES Production Function Model and Its Application in Calculating the Contribution Rate of Energy and Other Influencing Factors to Economic Growth," Journal of Systems Science and Information, De Gruyter, vol. 7(2), pages 161-172, April.
    4. A. Alessandri & L. Cassettari & R. Mosca, 2009. "Nonparametric nonlinear regression using polynomial and neural approximators: a numerical comparison," Computational Management Science, Springer, vol. 6(1), pages 5-24, February.
    5. Maolin Cheng, 2019. "A Grey CES Production Function Model and Its Application in Calculating the Contribution Rate of Economic Growth Factors," Complexity, Hindawi, vol. 2019, pages 1-8, April.
    6. Cui, Hengjian & Hu, Tao, 2011. "On nonlinear regression estimator with denoised variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1137-1149, February.
    7. Cheng Maolin, 2016. "A Generalized Constant Elasticity of Substitution Production Function Model and Its Application," Journal of Systems Science and Information, De Gruyter, vol. 4(3), pages 269-279, June.

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