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Linear wavelet estimation of the derivatives of a regression function based on biased data. (English) Zbl 1380.62140

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.

MSC:

62G07 Density estimation
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65T60 Numerical methods for wavelets
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