Abstract
Let X 1,X 2, … 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 L p -risk, 1 ≤ p < ∞, is considered. A kernel-type estimator f n based on X 1, …, X n 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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Stepanova, N. On estimation of analytic density functions in L p . Math. Meth. Stat. 22, 114–136 (2013). https://doi.org/10.3103/S1066530713020038
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DOI: https://doi.org/10.3103/S1066530713020038