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

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dc.contributor.authorKutovyi, V.
dc.contributor.authorKutovyi, O.
dc.contributor.authorShutovskyi, O.
dc.date.accessioned2022-06-07T08:16:32Z
dc.date.available2022-06-07T08:16:32Z
dc.date.issued2019
dc.description.abstractThe 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.uk_UA
dc.identifier.citationKutovyi 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.uk_UA
dc.identifier.issn2617-0264
dc.identifier.urihttps://repositary.knuba.edu.ua/handle/987654321/9666
dc.language.isoenuk_UA
dc.publisherKNUCAuk_UA
dc.subjecteconometric modeluk_UA
dc.subjectmatrix of incomplete rankuk_UA
dc.subjectGauss-Markov conditionsuk_UA
dc.subjectpseudoinverse matrixuk_UA
dc.subjectкафедра інформаційних технологій проєктування та прикладної математикиuk_UA
dc.subject.udc519.612uk_UA
dc.titleOn calculation of the pseudo-inverse econometric models matrix with a rank deficient observation matrixuk_UA
dc.title.alternativeО вычислении псевдообратной матрицы эконометрических моделей с матрицей наблюдений неполного рангаuk_UA
dc.typeArticleuk_UA

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Vol. 2, No.1