Open Access
November 2020 Estimation of Monge matrices
Jan-Christian Hütter, Cheng Mao, Philippe Rigollet, Elina Robeva
Bernoulli 26(4): 3051-3080 (November 2020). DOI: 10.3150/20-BEJ1215


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.


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Jan-Christian Hütter. Cheng Mao. Philippe Rigollet. Elina Robeva. "Estimation of Monge matrices." Bernoulli 26 (4) 3051 - 3080, November 2020.


Received: 1 July 2019; Revised: 1 March 2020; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256168
MathSciNet: MR4140537
Digital Object Identifier: 10.3150/20-BEJ1215

Keywords: constrained least-squares estimation , Monge matrices , permuted matrix estimation , Shape-constrained estimation

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 4 • November 2020
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