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Preliminary estimators for robust non-linear regression estimation

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  • Habshah Midi

Abstract

In this paper, the robustness of weighted non-linear least-squares estimation based on some preliminary estimators is examined. The preliminary estimators are the Lnorm estimates proposed by Schlossmacher, by El-Attar et al., by Koenker and Park, and by Lawrence and Arthur. A numerical example is presented to compare the robustness of the weighted non-linear least-squares approach when based on the preliminary estimators of Schlossmacher (HS), El-Attar et al. (HEA), Koenker and Park (HKP), and Lawrence and Arthur (HLA). The study shows that the HEA estimator is as robust as the HKP estimator. However, the HEA estimator posed certain computational problems and required more storage and computing time.

Suggested Citation

  • Habshah Midi, 1999. "Preliminary estimators for robust non-linear regression estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(5), pages 591-600.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:5:p:591-600
    DOI: 10.1080/02664769922250
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    1. Andre, Carmen D. S. & Peres, Clovis A. & Narula, Subhash C., 1992. "An algorithm for the MSAE estimation of the multistage dose-response model," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 293-299, October.
    2. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    3. Bassett, Gilbert W. & Koenker, Roger W., 1992. "A note on recent proposals for computing l1 estimates," Computational Statistics & Data Analysis, Elsevier, vol. 14(2), pages 207-211, August.
    4. Soliman, S. A. & Christensen, G. S. & Rouhi, A. H., 1991. "A new algorithm for nonlinear L1-norm minimization with nonlinear equality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 97-109, January.
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    Cited by:

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    2. Wenzhi Yang & Zhangrui Zhao & Xinghui Wang & Shuhe Hu, 2017. "The large deviation results for the nonlinear regression model with dependent errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 261-283, June.
    3. Yang, Wenzhi & Hu, Shuhe, 2014. "Large deviation for a least squares estimator in a nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 135-144.

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