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- W2903036966 abstract "This paper addresses a problem of estimating an additive functional given $n$ i.i.d. samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size $k$. The additive functional is defined as $theta(P;phi)=sum_{i=1}^kphi(p_i)$ for a function $phi$, which covers the most of the entropy-like criteria. The minimax optimal risk of this problem has been already known for some specific $phi$, such as $phi(p)=p^alpha$ and $phi(p)=-pln p$. However, there is no generic methodology to derive the minimax optimal risk for the additive function estimation problem. In this paper, we reveal the property of $phi$ that characterizes the minimax optimal risk of the additive functional estimation problem; this analysis is applicable to general $phi$. More precisely, we reveal that the minimax optimal risk of this problem is characterized by the divergence speed of the function $phi$." @default.
- W2903036966 created "2018-12-11" @default.
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- W2903036966 date "2018-11-28" @default.
- W2903036966 modified "2023-09-27" @default.
- W2903036966 title "Minimax Optimal Additive Functional Estimation with Discrete Distribution." @default.
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