Chaubey, Yogendra P.; Chesneau, Christophe; Navarro, Fabien Linear wavelet estimation of the derivatives of a regression function based on biased data. (English) Zbl 1380.62140 Commun. Stat., Theory Methods 46, No. 19, 9541-9556 (2017). Summary: This article deals with the problem of estimating the derivatives of a regression function based on biased data. We develop two different linear wavelet estimators according to the knowledge of the “biased density” of the design. The new estimators are analyzed with respect to their \(\mathbb{L}^p\)-risk with \(p\geq 1\) over Besov balls. Fast polynomial rates of convergence are obtained. Cited in 1 ReviewCited in 3 Documents MSC: 62G07 Density estimation 62G08 Nonparametric regression and quantile regression 62G20 Asymptotic properties of nonparametric inference 65T60 Numerical methods for wavelets Keywords:Besov balls; biased data; derivatives function estimation; nonparametric regression; wavelets PDFBibTeX XMLCite \textit{Y. P. Chaubey} et al., Commun. Stat., Theory Methods 46, No. 19, 9541--9556 (2017; Zbl 1380.62140) Full Text: DOI HAL