Nonparametric Wavelet Regression Based on Biased Data

Christophe Chesneau and Esmaeil Shirazi

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 13, 2642-2658

Abstract: The estimation of the regression function in the biased nonparametric regression model is investigated. We propose and develop a new wavelet-based methodology for this problem. In particular, an adaptive hard thresholding wavelet estimator is constructed. Under mild assumptions on the model, we prove that it enjoys powerful mean integrated squared error properties over Besov balls.

Date: 2014
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DOI: 10.1080/03610926.2012.681536

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