Abstract
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 < ∞, is considered. A kernel-type estimator fn based on X1, …, Xn is proposed and the upper bound on its asymptotic local maximum risk is established. Our result is consistent with a conjecture of Guerre and Tsybakov [7] and augments previous work in this area.
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