Adaptive estimation of the L2-norm of a probability density and related topics I. Lower bounds
概率密度 L2 范数的自适应估计及相关问题之一：下界
We deal with the problem of the adaptive estimation of the L2–norm of a probability density on Rd, d≥1, from independent observations. The unknown density is assumed to be uniformly bounded and to belong to the union of balls in the isotropic/anisotropic Nikolskii’s spaces. We will show that the optimally adaptive estimators over the collection of considered functional classes do no exist. Also, in the framework of an abstract density model we present several generic lower…