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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Keywords analytic density functions, kernel-type estimators, nonparametric density estimation
Persistent URL dx.doi.org/10.3103/S1066530713020038
Journal Mathematical Methods of Statistics
Stepanova, N. (2013). On estimation of analytic density functions in Lp. Mathematical Methods of Statistics, 22(2), 114–136. doi:10.3103/S1066530713020038