Open Access
2020 Optimal rates for estimation of two-dimensional totally positive distributions
Jan-Christian Hütter, Cheng Mao, Philippe Rigollet, Elina Robeva
Electron. J. Statist. 14(2): 2600-2652 (2020). DOI: 10.1214/20-EJS1729


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.


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Jan-Christian Hütter. Cheng Mao. Philippe Rigollet. Elina Robeva. "Optimal rates for estimation of two-dimensional totally positive distributions." Electron. J. Statist. 14 (2) 2600 - 2652, 2020.


Received: 1 March 2020; Published: 2020
First available in Project Euclid: 18 July 2020

zbMATH: 1446.62105
MathSciNet: MR4124557
Digital Object Identifier: 10.1214/20-EJS1729

Primary: 62G05 , 62G07

Keywords: Nonparametric density estimation , Shape-constrained estimation , Totally positive distributions

Vol.14 • No. 2 • 2020
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