Natalia Stepanova: Risk Bounds for the Estimation of Analytic Density Functions in Lp

Let X1,X2,... be a sequence of independent identically distributed random variables with an unknown density function f on R. The function f is assumed to belong to a certain class of analytic functions. The problem of estimation of f using Lp-risk, 1 < p < Inf, is considered. A kernel-type estimator fn based on X1,..., Xn is proposed and the upper bound on its limiting local minimax Lp-risk is established. Our result is consistent with a conjecture of Guerre and Tsybakov (Probab. Theory Relat. Fields 112 (1998) 33{51) and augments previous work in this area.