Optimal rates for estimation of two-dimensional totally positive distributions
Author(s)Hütter, Jan-Christian; Mao, Cheng; Rigollet, Philippe; Robeva, Elina
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© 2020, Institute of Mathematical Statistics. All rights reserved. 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 β-Hölder smooth densities where β ∈ (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.
Electronic Journal of Statistics
Institute of Mathematical Statistics