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, Volume 28, Issue 2, pp 369–398 | Cite as

Robust inference for nonlinear regression models

  • Ana M. BiancoEmail author
  • Paula M. Spano
Original Paper

Abstract

A family of weighted estimators of the regression parameter under a nonlinear model is introduced. The proposed weighted estimators are computed through a four-step MM-procedure, and the given approach allows for possible missing responses. Under mild conditions, the proposed estimators turn to be consistent and asymptotically normal. A robust Wald-type test statistic based on this family of estimators is also provided, and its asymptotic distribution is derived under the null and contiguous hypotheses. The local robustness of the proposed procedures is studied via the influence function analysis, and the finite sample behaviour of the estimators and tests is investigated through a Monte Carlo study in different contaminated scenarios. An application to an environmental data set illustrates the procedure.

Keywords

Nonlinear regression MM-procedure Robust estimation Robust hypothesis testing Missing at random 

Mathematics Subject Classification

MSC 62F35 MSC 62F10 MSC 62F03 

Notes

Acknowledgements

The authors thank the anonymous referees for their comments and suggestions that helped to improve the presentation. This research was partially supported by Grants pip 112-201101-00339 from conicet, pict 2014-0351 from anpcyt and 20020130100279ba from the Universidad de Buenos Aires at Buenos Aires, Argentina.

Supplementary material

11749_2017_570_MOESM1_ESM.pdf (1.7 mb)
Supplementary material 1 (pdf 1746 KB)

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2017

Authors and Affiliations

  1. 1.Instituto de Cálculo, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos Aires and CONICET, Ciudad UniversitariaBuenos AiresArgentina

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