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Penalization versus Goldenshluger − Lepski strategies in warped bases regression

Gaëlle Chagny — 2013

ESAIM: Probability and Statistics

This paper deals with the problem of estimating a regression function , in a random design framework. We build and study two adaptive estimators based on model selection, applied with warped bases. We start with a collection of finite dimensional linear spaces, spanned by orthonormal bases. Instead of expanding directly the target function on these bases, we rather consider the expansion of  =  ∘ , where is the cumulative distribution function of the design, following Kerkyacharian...

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