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Register a new userOptimal Rates for Estimation of Two-Dimensional Totally Positive Distributions
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Added by
Cheng Mao
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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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 $beta$-Holder 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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