Наближені гарантовані оцінки матриць у задачах лінійної регресії з малим параметром

• Видавець: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
• Дата: 2020
• Автори: Nakonechnyi, Oleksandr, Kudin, Grygoriy, Zinko, Petro, Zinko, Taras
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2020
• Теми: линейное оценивание; несмещенные оценки; гарантированная среднеквадратическая погрешность; линейные операторные уравнения; псевдообратные матрицы; малый параметр; возмущенные известные матрицы наблюдения; linear estimation; unbiased estimates; guaranteed mean square error; linear operator equations; pseudo inverse matrices; small parameter; perturbed known observation matrices; лінійне оцінювання; незміщені оцінки; гарантована середньоквадратична похибка; лінійні операторні рівняння; псевдообернені матриці; малий параметр; збурені відомі матриці спостереження
• Онлайн доступ: http://journal.iasa.kpi.ua/article/view/228376

The problem of finding linear unbiased estimates of the linear operator of unknown matrices — components of the observations vector, is investigated. It is assumed that the observation vector additively depends on a random vector with zero expected value, and the unknown correlation matrix belongs to a known bounded set. For the introduced class of linear estimates, necessary and sufficient conditions for the existence of solutions of operator equations that determine the unknown parameters of the vector estimate, are proved. The form of the guaranteed mean square error of the estimate is introduced on the sets of constraints of the problem parameters. The influence on the linear unbiased estimate of small perturbations of known rectangular matrices, which are the composites of the observations vector components, is also investigated. The analytical form is given through the parameters of the perturbed set of singularities for the introduced special operators that depend on a small parameter, which determine the corresponding operator equations, as well as their approximate solutions, in the first approximation of the small parameter method. A test example of solving the problem of finding a linear unbiased estimate under the condition of perturbation of both linearly independent and linearly dependent known observation matrices is presented.