On calculation of the pseudo-inverse econometric models matrix with a rank deficient observation matrix

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Ескіз
Дата
2019
Автори
Kutovyi, V.
Kutovyi, O.
Shutovskyi, O.
Заголовок журналу
Журнал ISSN
Назва тому
Видавець
KNUCA
Анотація
The approach to estimating the parameters of linear econometric dependencies for the case of combining a number of special conditions arising in the modeling process is considered. These conditions concern the most important problems that arise in practice when implementing a number of classes of mathematical models, for the construction of which a matrix of explanatory variables is used. In most cases, the vectors that make up the matrix have a close correlation relationship. That leads to the need to perform calculations using a rank deficient matrix. There are also violations of the conditions of the Gauss-Markov theorem. For any non-degenerate square matrix X, an inverse matrix X-1 is uniquely defined such that, for random right-hand side B , the solution of the system X β = B is vector β X-1 b . If X is a degenerate or rectangular matrix, then there is no inverse to it. Moreover, in these cases, the system X β = B may be incompatible. Here it is natural to use a generalization of the concept of the inverse transformation, which is formulated in terms of the corresponding problem of minimizing the sum of squared residuals. In the same case, having a QR decomposition, one can use the formula X+ = R-1 Q1’. In addition, it is recommended for specific calculations. With an incomplete rank, the most convenient form of representation 1 X-1 follows from the expansion in characteristic numbers. If X = U ΣV with non-zero characteristic numbers, then X+ = VΣ+U’. We propose an alternative X+ calculation method, which relies on the decomposition of a rank deficient matrix into the product of two matrices of full rank.
Опис
Ключові слова
econometric model, matrix of incomplete rank, Gauss-Markov conditions, pseudoinverse matrix, кафедра інформаційних технологій проєктування та прикладної математики
Бібліографічний опис
Kutovyi V. On calculation of the pseudo-inverse econometric models matrix with a rank deficient observation matrix / V. Kutovyi, O. Kutovyi, O. Shutovskyi // Transfer of innovative technologies = Трансфер інформаційних технологій : international scientific journal / KNUCA ; editor-in-chief М. Sukach - Kyiv : Lira-K, 2019. - Vol. 2(1). – P. 68 - 74 - Bibliogr. : 21 titl.
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