Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimation of Monge Matrices   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.

12
The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat