Abstract
Based on a data-driven selection of an estimator from a fixed family of
kernel estimators, Goldenshluger \& Lepski (2014)
considered the problem of adaptive minimax un-compactly supported
density estimation on $\mathbb{R}^{d}$ with
$L^{p}$ risk over Nikol’skii classes. This paper shows the same
convergence rates by using a data-driven wavelet estimator over Besov
spaces, because the wavelet estimations provide more local information
and fast algorithm. Moreover, we provide better convergence rates under
the independence hypothesis, which reduces the dimension disaster
effectively.