Minimax estimation of norms of a probability density: II. Rate-optimal estimation procedures

In this paper we develop rate–optimal estimation procedures in the problem of estimating Lp–norm, p∈(1,∞) a probability density from independent observations. The is assumed to be defined on Rd, d≥1 and belong ball anisotropic Nikolskii space. We adopt minimax approach construct estimators case integer p≥2. demonstrate that, depending parameters class norm index p, rates convergence may vary inconsistency parametric n–estimation. results complement lower bounds derived companion (Goldenshluger Lepski (2020)).