文章基本信息

标题：Optimal rates for estimation of two-dimensional totally positive distributions
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作者：Jan-Christian Hütter ; Cheng Mao ; Philippe Rigollet 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：2
页码：2600-2652
DOI：10.1214/20-EJS1729
语种：English
出版社：Institute of Mathematical Statistics
摘要：We study minimax estimation of two-dimensional totally positive distributions. Such distributions pertain to pairs of strongly positively dependent random variables and appear frequently in statistics and probability. In particular, for distributions with $\beta$-Hölder smooth densities where $\beta\in(0,2)$, we observe polynomially faster minimax rates of estimation when, additionally, the total positivity condition is imposed. Moreover, we demonstrate fast algorithms to compute the proposed estimators and corroborate the theoretical rates of estimation by simulation studies.
关键词：Totally positive distributions; nonparametric density estimation; shape-constrained estimation