The purpose of this paper is the totally adaptive estimation using data-driven wavelet method. New theoretical contributions are provided for biased density function with un-compactly support; \(L^p\) convergence rates of data-driven wavelet estimators are established in the Besov space \(B^{s}_{r,q}(\mathbb {R}^d)\) . Firstly, a data driven wavelet estimator is constructed for the biased density on \(\mathbb {R}^d\) . Subsequently, a point-wise oracle inequality is provided for proving our results. Finally, upper bounds of \(L^p\) risks are discussed from four different zones. It is verified that the proposed data-driven wavelet estimator is approximately optimal. Specially, compared to the linear and nolinear wavelet estimators, data-driven wavelet estimator is shown to be totally adaptive.
