{"title":"A Short Information-Theoretic Analysis of Linear Auto-Regressive Learning","authors":"Ingvar Ziemann","doi":"arxiv-2409.06437","DOIUrl":null,"url":null,"abstract":"In this note, we give a short information-theoretic proof of the consistency\nof the Gaussian maximum likelihood estimator in linear auto-regressive models.\nOur proof yields nearly optimal non-asymptotic rates for parameter recovery and\nworks without any invocation of stability in the case of finite hypothesis\nclasses.","PeriodicalId":501175,"journal":{"name":"arXiv - EE - Systems and Control","volume":"5 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - EE - Systems and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06437","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we give a short information-theoretic proof of the consistency
of the Gaussian maximum likelihood estimator in linear auto-regressive models.
Our proof yields nearly optimal non-asymptotic rates for parameter recovery and
works without any invocation of stability in the case of finite hypothesis
classes.
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