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M-estimation for the partially linear regression model under monotonic constraints

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  • Du, Jiang
  • Sun, Zhimeng
  • Xie, Tianfa

Abstract

In this paper, we study M-estimation for the partially linear model under monotonic constraints. We use monotone B-splines to approximate the monotone nonparametric function. We show the large sample properties of the resulting estimators. The proposed estimator of parameter part is root-n consistent, and asymptotically normal and the estimator for the nonparametric component achieves the optimal convergence rate. A simulation study is conducted to evaluate the finite sample performance of the method. The proposed procedure is illustrated by an air pollution study.

Suggested Citation

  • Du, Jiang & Sun, Zhimeng & Xie, Tianfa, 2013. "M-estimation for the partially linear regression model under monotonic constraints," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1353-1363.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:5:p:1353-1363
    DOI: 10.1016/j.spl.2013.01.006
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    References listed on IDEAS

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    Cited by:

    1. Graciela Boente & Daniela Rodriguez & Pablo Vena, 2020. "Robust estimators in a generalized partly linear regression model under monotony constraints," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 50-89, March.

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