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Title: Optimal estimation of bacterial growth rates based on a permuted monotone matrix
Summary Motivated by the problem of estimating bacterial growth rates for genome assemblies from shotgun metagenomic data, we consider the permuted monotone matrix model $Y=\Theta\Pi+Z$ where $Y\in \mathbb{R}^{n\times p}$ is observed, $\Theta\in \mathbb{R}^{n\times p}$ is an unknown approximately rank-one signal matrix with monotone rows, $\Pi \in \mathbb{R}^{p\times p}$ is an unknown permutation matrix, and $Z\in \mathbb{R}^{n\times p}$ is the noise matrix. In this article we study estimation of the extreme values associated with the signal matrix $\Theta$, including its first and last columns and their difference. Treating these estimation problems as compound decision problems, minimax rate-optimal estimators are constructed using the spectral column-sorting method. Numerical experiments on simulated and synthetic microbiome metagenomic data are conducted, demonstrating the superiority of the proposed methods over existing alternatives. The methods are illustrated by comparing the growth rates of gut bacteria in inflammatory bowel disease patients and control subjects.  more » « less
Award ID(s):
2015259
NSF-PAR ID:
10340063
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Biometrika
Volume:
108
Issue:
3
ISSN:
0006-3444
Page Range / eLocation ID:
693 to 708
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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