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Robust inference for nonlinear regression models

Author

Listed:
  • Ana M. Bianco

    (Universidad de Buenos Aires and CONICET, Ciudad Universitaria)

  • Paula M. Spano

    (Universidad de Buenos Aires and CONICET, Ciudad Universitaria)

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.

Suggested Citation

  • Ana M. Bianco & Paula M. Spano, 2019. "Robust inference for nonlinear regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 369-398, June.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:2:d:10.1007_s11749-017-0570-2
    DOI: 10.1007/s11749-017-0570-2
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    References listed on IDEAS

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    1. Maronna, Ricardo A. & Yohai, Victor J., 2010. "Correcting MM estimates for "fat" data sets," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3168-3173, December.
    2. Bianco, Ana M. & Boente, Graciela & Rodrigues, Isabel M., 2013. "Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 209-226.
    3. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    4. Chen, Qingxia & Ibrahim, Joseph G. & Chen, Ming-Hui & Senchaudhuri, Pralay, 2008. "Theory and inference for regression models with missing responses and covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1302-1331, July.
    5. Christophe Croux & Mohammed Fekri & Anne Ruiz-Gazen, 2010. "Fast and robust estimation of the multivariate errors in variables model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 286-303, August.
    6. Sakata, Shinichi & White, Halbert, 2001. "S-estimation of nonlinear regression models with dependent and heterogeneous observations," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 5-72, July.
    7. Gallant, A. Ronald, 1975. "Seemingly unrelated nonlinear regressions," Journal of Econometrics, Elsevier, vol. 3(1), pages 35-50, February.
    8. Croux, Christophe, 1994. "Efficient high-breakdown M-estimators of scale," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 371-379, April.
    9. Bianco, Ana & Boente, Graciela, 2002. "On the asymptotic behavior of one-step estimates in heteroscedastic regression models," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 33-47, November.
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    Cited by:

    1. Francesco Bravo, 2020. "Robust estimation and inference for general varying coefficient models with missing observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 966-988, December.
    2. Mariela Sued & Marina Valdora & Víctor Yohai, 2020. "Robust doubly protected estimators for quantiles with missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 819-843, September.

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