Гарантовані середньоквадратичні оцінки прогнозу матричних спостережень в умовах статистичної невизначеності

• Date: 2023
• Main Authors: Nakonechnyi, Oleksandr, Kudin, Grygoriy, Zinko, Petro, Zinko, Taras
• Format: Article
• Language: English
• Published: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2023
• Subjects: матричні спостереження; лінійне оцінювання; гарантована середньоквадратична оцінка; похибка гарантованої середньоквадратичної оцінки; квазімінімаксна гарантована оцінка вектора; різницеве рівняння; метод малого параметра; збурення матриць
• Online Access: http://journal.iasa.kpi.ua/article/view/272758
• Journal Title: System research and information technologies

We investigate the problem of linear estimation of unknown mathematical expectations based on observations of realizations of random matrix sequences. Constructive mathematical methods have been developed for finding linear guaranteed RMS estimates of unknown non-stationary parameters of average values based on observations of realizations of random matrix sequences. It is shown that such guaranteed estimates are obtained either as solutions to boundary value problems for systems of linear differential equations or as solutions to the corresponding Cauchy problems. We establish the form and look for errors for the guaranteed RMS quasi-minimax estimates of the special forecast vector and parameters of unknown average values. In the presence of small perturbations of known matrices in the model of matrix observations, quasi-minimax RMS estimates are found, and their guaranteed RMS errors are obtained in the first approximation of the small parameter method. Two test examples for calculating the guaranteed root mean square estimates and their errors are given.