A not sign-preserving iteration algorithm for the 'Improved Normalized Squared Differences' matrix adjustment model


          

刊名：Central European journal of operations research: CEJOR
作者：Revesz, Tamas（Corvinus Univ Budapest）
刊号：270E0018
ISSN：1435-246X
出版年：2023
年卷期：2023, vol.31, no.1
页码：49-71
总页数：23
分类号：F
关键词：Biproportional matrix adjustment；Mathematical programming；Least squares；Distance function；Reference matrix；RAS-method；Sign flip；MARGINAL TOTALS；INFORMATION；TABLE
参考中译：
语种：eng
文摘：Estimating the elements of a matrix, when only the margins (row and column sums) are known, but a supposedly similar 'reference matrix' is available, is a standard problem in many disciplines. After discussing the main types, issues and applications of these two-directional matrix adjustment problems the paper concentrates on the case of negative matrix elements and models with quadratic objective functions. The solution of the Improved Normalized Squared Differences (INSD) model is proved to be the same as the result of that iteration algorithm which is presented in the paper. It is also argued that if the sign-preservation requirement is dropped then the iteration procedure suggested by Huang et al. (Econ Syst Res 20(1):111-123, 2008) boils down to the same algorithm. Using the numerical example of the earlier literature it is also demonstrated that even in this not sign-preserving case, which even requires sign-flips for some elements, the INSD-model produces good fit in mathematical terms.



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