On the Reynaud-Bouret–Rivoirard–Tuleau-Malot problem

Abstract

By using biorthogonal wavelets, Reynaud-Bouret, Rivoirard and Tuleau-Malot provide the adaptive and optimal [Formula: see text]-risk estimation for density functions (not necessarily having compact support) in a Besov space [Formula: see text] [P. Reynaud-Bouret, V. Rivoirard and C. Tuleau-Malot, Adaptive density estimation: A curse of support?, J. Stat. Plan. Inference 141(1) (2011) 115–139]. The authors pose an open problem: Can [Formula: see text]-risk ([Formula: see text]) estimation be given in their setting? In this paper, we try to solve that problem for [Formula: see text] by using wavelet estimators.