Optimal rates for estimation of two-dimensional totally positive distributions
Name
20-EJS1729.pdf
Description
Published version
Size
887.66 KB
Format
Adobe PDF
Checksum (MD5)
2c3924756bb9bb87b8c2d2e0805b1e8c
Author(s)
Hütter, Jan-Christian
Mao, Cheng
Rigollet, Philippe
Robeva, Elina
Date Issued
2020
Journal
Electronic Journal of Statistics
Publisher
Institute of Mathematical Statistics
Version
Final published version
Abstract
© 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/20-EJS1729
