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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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    1. Arcones, Miguel A., 1996. "The Bahadur-Kiefer Representation of Lp Regression Estimators," Econometric Theory, Cambridge University Press, vol. 12(02), pages 257-283, June.
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