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Estimating nonlinear regression with and without change-points by the LAD method

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Abstract

The paper considers the least absolute deviations estimator in a nonlinear parametric regression. The interest of the LAD method is its robustness with respect to other traditional methods when the errors of model contain outliers. First, in the absence of change-points, the convergence rate of estimated parameters is found. For a model with change-points, in the case when the number of jumps is known, the convergence rate and the asymptotic distribution of estimators are obtained. Particularly, it is shown that the change-points estimator converges weakly to the minimizer of given random process. Next, when the number of jumps is unknown, its consistent estimator is proposed, via the modified Schwarz criterion.

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Authors and Affiliations

  1. Institut Camille Jordan, Université de Lyon, CNRS, UMR 5208, Université Lyon 1, Bat. Braconnier, 43, blvd du 11 novembre 1918, 69622, Villeurbanne Cedex, France

    Gabriela Ciuperca

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  1. Gabriela Ciuperca
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Correspondence to Gabriela Ciuperca.

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Ciuperca, G. Estimating nonlinear regression with and without change-points by the LAD method. Ann Inst Stat Math 63, 717–743 (2011). https://doi.org/10.1007/s10463-009-0256-y

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  • DOI: https://doi.org/10.1007/s10463-009-0256-y

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