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Minimax Optimal Estimators for Additive Scalar Functionals of Discrete Distributions
[article]
2017
arXiv
pre-print
In this paper, we consider estimators for an additive functional of ϕ, which is defined as θ(P;ϕ)=∑_i=1^kϕ(p_i), from n i.i.d. random samples drawn from a discrete distribution P=(p_1,...,p_k) with alphabet size k. We propose a minimax optimal estimator for the estimation problem of the additive functional. We reveal that the minimax optimal rate is characterized by the divergence speed of the fourth derivative of ϕ if the divergence speed is high. As a result, we show there is no consistent
arXiv:1701.06381v3
fatcat:bcddnbm55jfkdk4i3o5shxrlcy