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pp 1–40 | Cite as

Robust estimators in a generalized partly linear regression model under monotony constraints

  • Graciela BoenteEmail author
  • Daniela Rodriguez
  • Pablo Vena
Original Paper

Abstract

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and nonparametrically on an univariate regressor in such a way that the nonparametric component is assumed to be a monotone function. A class of robust estimates for the monotone nonparametric component and for the regression parameter, related to the linear one, is defined. The robust estimators are based on a spline approach combined with a score function which bounds large values of the deviance. As an application, we consider the isotonic partly linear log-Gamma regression model. Under regularity conditions, we derive consistency results for the nonparametric function estimators as well as consistency and asymptotic distribution results for the regression parameter estimators. Besides, the empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. Through a Monte Carlo study, we investigate the performance of the proposed estimators under a partly linear log-Gamma regression model with increasing nonparametric component. The proposal is illustrated on a real data set.

Keywords

B-splines Deviance Isotonic regression Partial linear models Robust estimation 

Mathematics Subject Classification

62F30 62G35 

Notes

Acknowledgements

The authors wish to thank the Associate Editor and two anonymous referee for their valuable comments which led to an improved version of the original paper. This research was partially supported by Grants pip 112-201101-00742 from conicet, pict 2014-0351 from anpcyt and 20020170100022BA and 20020170100330BA from the Universidad de Buenos Aires, Argentina and also by the Spanish Project MTM2016-76969P from the Ministry of Science and Innovation, Spain.

Supplementary material

11749_2019_629_MOESM1_ESM.pdf (1.2 mb)
Supplementary material. The supplementary material (available online) contains the proof of Theorem 3 and that of the expressions given in (21) and (22) for the empirical influence function of the proposed estimators. Some additional figures for the empirical influence function given in Section 6.1 are provided. It also contains some lemmas ensuring that the entropy assumptions C4 and C5 hold, for some choices of the loss function. 1.21MB PDF

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  • Graciela Boente
    • 1
    Email author
  • Daniela Rodriguez
    • 2
  • Pablo Vena
    • 1
  1. 1.Departamento de Matemáticas, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos Aires and CONICETBuenos AiresArgentina
  2. 2.Instituto de Cálculo, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos Aires and CONICETBuenos AiresArgentina

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