An extension of Chesneau’s theorem

This paper considers a lower bound estimation over Lp(Rd)(1≤p<∞) risk for dd dimensional regression functions in Besov spaces based on biased data. We provide the best possible lower bound up to a lnnlnn factor by using wavelet methods. When the weight function ω(x,y)≡1ω(x,y)≡1 and d=1d=1, our result reduces to Chesneau’s theorem, see Chesneau (2007).