{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T01:24:19Z","timestamp":1777512259808,"version":"3.51.4"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2020,10,8]],"date-time":"2020-10-08T00:00:00Z","timestamp":1602115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,8,12]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1093\/biomet\/asaa082","type":"journal-article","created":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T19:13:46Z","timestamp":1600888426000},"page":"693-708","source":"Crossref","is-referenced-by-count":8,"title":["Optimal estimation of bacterial growth rates based on a permuted monotone matrix"],"prefix":"10.1093","volume":"108","author":[{"given":"Rong","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T Tony","family":"Cai","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongzhe","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,10,8]]},"reference":[{"key":"2021081218511515400_B1","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1038\/nmeth.3253","article-title":"Sequence tag\u2013based analysis of microbial population dynamics","volume":"12","author":"Abel,","year":"2015","journal-title":"Nature Meth."},{"key":"2021081218511515400_B2","doi-asserted-by":"publisher","DOI":"10.1038\/s41587-020-0603-3","article-title":"A unified catalog of 204,938 reference genomes from the human gut microbiome","volume":"38","author":"Almeida,","year":"2020","journal-title":"Nature Biotechnol."},{"key":"2021081218511515400_B3","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/B978-0-08-102268-9.00004-5","article-title":"Computational and statistical considerations in the analysis of metagenomic data","author":"Boulund,","year":"2018","journal-title":"Metagenomics"},{"key":"2021081218511515400_B4","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/0022-5193(77)90373-3","article-title":"An examination of the Cooper-Helmstetter theory of DNA replication in bacteria and its underlying assumptions","volume":"69","author":"Bremer,","year":"1977","journal-title":"J. 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