Estimation of Monge matrices
Name
1904.03136.pdf
Description
Submitted version
Size
1.89 MB
Format
Adobe PDF
Checksum (MD5)
2693676b35e89fdb3fc0803b96042009
Author(s)
Hütter, Jan-Christian
Mao, Cheng
Rigollet, Philippe
Robeva, Elina
Date Issued
2020
Journal
Bernoulli
Publisher
Bernoulli Society for Mathematical Statistics and Probability
Version
Original manuscript
Abstract
© 2020 ISI/BS. Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such matrices have long been leveraged for algorithmic purposes, little is known about their impact on statistical estimation. In this work, we propose to view this structure as a shape constraint and study the problem of estimating a Monge matrix subject to additive random noise. More specifically, we establish the minimax rates of estimation of Monge and pre-Monge matrices. In the case of pre-Monge matrices, the minimax-optimal least-squares estimator is not efficiently computable, and we propose two efficient estimators and establish their rates of convergence. Our theoretical findings are supported by numerical experiments.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3150/20-BEJ1215
