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Regression with random design: a minimax study. (English) Zbl 1109.62028

Summary: The problem of estimating a regression function based on a regression model with (known) random design is considered. By adopting the framework of wavelet analysis, we establish the asymptotic minimax rate of convergence under the \(\mathbb L^p\) risk over Besov balls. A part of this paper is devoted to the case where the design density is vanishing.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
46N30 Applications of functional analysis in probability theory and statistics
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