IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v28y2019i2d10.1007_s11749-017-0570-2.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-017-0570-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-017-0570-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Gallant, A. Ronald, 1975. "Seemingly unrelated nonlinear regressions," Journal of Econometrics, Elsevier, vol. 3(1), pages 35-50, February.
    5. 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.
    6. 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.
    7. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    8. 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.
    9. Croux, Christophe, 1994. "Efficient high-breakdown M-estimators of scale," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 371-379, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tao Wang, 2024. "Nonlinear kernel mode‐based regression for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 189-213, March.
    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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bianco, Ana M. & Spano, Paula M., 2017. "Robust estimation in partially linear errors-in-variables models," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 46-64.
    2. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    3. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 237-274.
    4. Matthew Gentzkow, 2007. "Valuing New Goods in a Model with Complementarity: Online Newspapers," American Economic Review, American Economic Association, vol. 97(3), pages 713-744, June.
    5. Greg Kaplan, 2012. "Inequality and the life cycle," Quantitative Economics, Econometric Society, vol. 3(3), pages 471-525, November.
    6. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
    7. Rania Gihleb & Osnat Lifshitz, 2022. "Dynamic Effects of Educational Assortative Mating on Labor Supply," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 46, pages 302-327, October.
    8. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    9. Aslanidis, Nektarios, 2007. "Business Cycle Regimes in CEECs Production: A Threshold SURE Approach," Working Papers 2072/5318, Universitat Rovira i Virgili, Department of Economics.
    10. John M. Abowd & Francis Kramarz & Sébastien Pérez-Duarte & Ian M. Schmutte, 2018. "Sorting Between and Within Industries: A Testable Model of Assortative Matching," Annals of Economics and Statistics, GENES, issue 129, pages 1-32.
    11. Mariacristina De Nardi & Eric French & John Bailey Jones, 2016. "Medicaid Insurance in Old Age," American Economic Review, American Economic Association, vol. 106(11), pages 3480-3520, November.
    12. Haaijer, Marinus E., 1996. "Predictions in conjoint choice experiments : the x-factor probit model," Research Report 96B22, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    13. Igal Hendel, 1994. "Estimating Multiple-Discrete Choice Models: An Application to Computeri-zzation Returns," NBER Technical Working Papers 0168, National Bureau of Economic Research, Inc.
    14. Charlier, Erwin & Melenberg, Bertrand & van Soest, Arthur, 2000. "Estimation of a censored regression panel data model using conditional moment restrictions efficiently," Journal of Econometrics, Elsevier, vol. 95(1), pages 25-56, March.
    15. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    16. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    17. Wei Huang & Oliver Linton & Zheng Zhang, 2022. "A Unified Framework for Specification Tests of Continuous Treatment Effect Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1817-1830, October.
    18. Calvet, Laurent E. & Czellar, Veronika, 2015. "Through the looking glass: Indirect inference via simple equilibria," Journal of Econometrics, Elsevier, vol. 185(2), pages 343-358.
    19. Keane, Michael & Moffitt, Robert, 1998. "A Structural Model of Multiple Welfare Program Participation and Labor Supply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 553-589, August.
    20. Yi Deng, 2003. "A Dynamic Stochastic Analysis of International Patent Application and Renewal Processes," Computing in Economics and Finance 2003 189, Society for Computational Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:28:y:2019:i:2:d:10.1007_s11749-017-0570-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.