Statistics and Computing

, Volume 17, Issue 4, pp 293–310 | Cite as

Robust estimation and wavelet thresholding in partially linear models

  • Irène GannazEmail author


This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We present a wavelet thresholding based estimation procedure to estimate the components of the partial linear model by establishing a connection between an l 1-penalty based wavelet estimator of the nonparametric component and Huber’s M-estimation of a standard linear model with outliers. Some general results on the large sample properties of the estimates of both the parametric and the nonparametric part of the model are established. Simulations are used to illustrate the general results and to compare the proposed methodology with other methods available in the recent literature.


Semi-nonparametric models Partially linear models Wavelet thresholding Backfitting M-estimation Penalized least-squares 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Laboratoire de Modélisation et CalculUniversité Joseph FourierGrenoble Cedex 9France

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