{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T12:49:31Z","timestamp":1776430171633,"version":"3.51.2"},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T00:00:00Z","timestamp":1622764800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:p>For an <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000177_inline1.png\"\/><jats:tex-math>$N \\times T$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> random matrix \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000177_inline2.png\"\/><jats:tex-math>\n$X(\\beta )$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with weakly dependent uniformly sub-Gaussian entries \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000177_inline3.png\"\/><jats:tex-math>\n$x_{it}(\\beta )$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> that may depend on a possibly infinite-dimensional parameter \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000177_inline4.png\"\/><jats:tex-math>\n$\\beta \\in \\mathbf {B}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, we obtain a uniform bound on its operator norm of the form \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000177_inline5.png\"\/><jats:tex-math>\n$\\mathbb {E} \\sup _{\\beta \\in \\mathbf {B}} ||X(\\beta )|| \\leq CK \\left (\\sqrt {\\max (N,T)} + \\gamma _2(\\mathbf {B},d_{\\mathbf {B}})\\right )$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, where <jats:italic>C<\/jats:italic> is an absolute constant, <jats:italic>K<\/jats:italic> controls the tail behavior of (the increments of) \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000177_inline6.png\"\/><jats:tex-math>\n$x_{it}(\\cdot )$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, and \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000177_inline7.png\"\/><jats:tex-math>\n$\\gamma _2(\\mathbf {B},d_{\\mathbf {B}})$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is Talagrand\u2019s functional, a measure of multiscale complexity of the metric space \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000177_inline8.png\"\/><jats:tex-math>\n$(\\mathbf {B},d_{\\mathbf {B}})$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We illustrate how this result may be used for estimation that seeks to minimize the operator norm of moment conditions as well as for estimation of the maximal number of factors with functional data.<\/jats:p>","DOI":"10.1017\/s0266466621000177","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T08:55:36Z","timestamp":1622796936000},"page":"1073-1091","source":"Crossref","is-referenced-by-count":1,"title":["A UNIFORM BOUND ON THE OPERATOR NORM OF SUB-GAUSSIAN RANDOM MATRICES AND ITS APPLICATIONS"],"prefix":"10.1017","volume":"38","author":[{"given":"Grigory","family":"Franguridi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hyungsik Roger","family":"Moon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,6,4]]},"reference":[{"key":"S0266466621000177_r14","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2017.1279058"},{"key":"S0266466621000177_r17","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-008-0034-1"},{"key":"S0266466621000177_r1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2014.909317"},{"key":"S0266466621000177_r3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0661-8"},{"key":"S0266466621000177_r21","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/132"},{"key":"S0266466621000177_r18","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466615000328"},{"key":"S0266466621000177_r20","volume-title":"The Generic Chaining: Upper and Lower Bounds of Stochastic Processes","author":"Talagrand","year":"2006"},{"key":"S0266466621000177_r24","volume-title":"High-Dimensional Probability: An Introduction with Applications in Data Science","volume":"47","author":"Vershynin","year":"2018"},{"key":"S0266466621000177_r19","unstructured":"Shalizi, C. & Kontorovich, A. 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