Natalia Stepanova: Risk Bounds for the Estimation of Analytic Density Functions in Lp
Natalia Stepanova, Carleton University, Canada
Time: Wed 2014-06-11 13.15 - 14.15
Location: Room 3721, Lindstedtsvägen 25, 7th floor, Department of Mathematics
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.