МЕТОД ЗБУРЕННЯ В ЗАДАЧАХ ЛІНІЙНОЇ МАТРИЧНОЇ РЕГРЕСІЇ

• Datum: 2020
• Hauptverfasser: Nakonechnyi, A.G., Kudin, G.I., Zinko, P.N., Zinko, T.Р.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Schlagworte: метод збурення; малий параметр; лінійна регресія; операторні рівняння; незміщувані оцінки; матриці спостережень; псевдообернені матриці
• Online Zugang: https://jais.net.ua/index.php/files/article/view/444
• Назва журналу: Problems of Control and Informatics

In the framework of the theory of linear regression, linear from observations estimates are studied, in particular, the unbiased estimates, which lead to unbiased equations, among which the solutions are distinguished by the minimum norm, which allows to minimize the mean square error for non-correlated observation errors with the same variances. Preliminarily, the task of linear regression analysis is represented as a linear operator in the space of independent rectangular matrices associated with the equation of unbiased of linear functions of matrix parameters. It is assumed that for this operator in the unperturbed version its SVD representation is known, as well as SVD representation for the pseudo inverse to it operator. Taking into account the need to determine the singular set of the perturbed operator, the perturbation method is used to determine the eigenvalues and eigenvectors of the special symmetric matrix, according to the general theory of operators in Euclidean space the eigenmatrices of the adjoint perturbed operator are determined. Assuming that the linear regression analysis problem in the presence of matrix perturbations of the observation can be solved in real time, the resulting formulas are presented in a first approximation of a small parameter. A test example in which, in addition to a small parameter, the parameters of random perturbations also enter, is given.