文摘
Let (Xi)i≥1 be an i.i.d. sample on having density f. Given a real function on with finite variation, and given an integer valued sequence (jn), let denote the estimator of f by wavelet projection based on and with multiresolution level equal to jn. We provide exact rates of almost certain convergence to 0 of the quantity , when n2−djn/logn→∞ and H is a given hypercube of . We then show that, if n2−djn/logn→c for a constant c>0, then the quantity almost surely fails to converge to 0.