{"title":"Non-Asymptotic Confidence Estimation of the Autoregressive Process Paremeters in the Case of an Unknown Noise Variance","authors":"S. E. Vorobeychikov, A. V. Pupkov","doi":"10.3103/s8756699023040106","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A non-asymptotic procedure of constructing the confidence region of the parameter of the <span>\\(p\\)</span>-th order Gaussian autoregressive process AR(p) in the case of an unknown process noise variance is considered. The confidence estimation procedure is based on the martingale property of the numerator of estimate deviation of the least square technique (LST). The results of numerical modeling are presented.</p>","PeriodicalId":44919,"journal":{"name":"Optoelectronics Instrumentation and Data Processing","volume":"244 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optoelectronics Instrumentation and Data Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s8756699023040106","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
A non-asymptotic procedure of constructing the confidence region of the parameter of the \(p\)-th order Gaussian autoregressive process AR(p) in the case of an unknown process noise variance is considered. The confidence estimation procedure is based on the martingale property of the numerator of estimate deviation of the least square technique (LST). The results of numerical modeling are presented.
期刊介绍：
The scope of Optoelectronics, Instrumentation and Data Processing encompasses, but is not restricted to, the following areas: analysis and synthesis of signals and images; artificial intelligence methods; automated measurement systems; physicotechnical foundations of micro- and optoelectronics; optical information technologies; systems and components; modelling in physicotechnical research; laser physics applications; computer networks and data transmission systems. The journal publishes original papers, reviews, and short communications in order to provide the widest possible coverage of latest research and development in its chosen field.
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