{"title":"Hidden AR process and adaptive Kalman filter","authors":"Yury A. Kutoyants","doi":"10.1007/s10463-024-00908-7","DOIUrl":null,"url":null,"abstract":"<p>This work discusses a model of a partially observed linear system that depends on some unknown parameters. An approximation of the unobserved component is proposed, which involves three steps. First, a method of moment estimator of unknown parameters is constructed, and second, this estimator is used to define the one-step MLE-process. Finally, the last estimator is substituted into the equations of the Kalman filter. The solution of obtained equations provides us with the desired approximation (adaptive Kalman filter). The asymptotic properties of all the mentioned estimators and both maximum likelihood and Bayesian estimators of the unknown parameters are detailed. The asymptotic efficiency of adaptive filtering is discussed.</p>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the Institute of Statistical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10463-024-00908-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
This work discusses a model of a partially observed linear system that depends on some unknown parameters. An approximation of the unobserved component is proposed, which involves three steps. First, a method of moment estimator of unknown parameters is constructed, and second, this estimator is used to define the one-step MLE-process. Finally, the last estimator is substituted into the equations of the Kalman filter. The solution of obtained equations provides us with the desired approximation (adaptive Kalman filter). The asymptotic properties of all the mentioned estimators and both maximum likelihood and Bayesian estimators of the unknown parameters are detailed. The asymptotic efficiency of adaptive filtering is discussed.
期刊介绍:
Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.