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Erschienen in:
2020 | OriginalPaper | Buchkapitel
Method of Parametric Correction in Data Transformation and Approximation Problems
verfasst von : Victor Gorelik, Tatiana Zolotova
Erschienen in: Optimization and Applications
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Abstract
The linear regression analysis problems are considered under the assumption of the presence of noise in the output and input variables. To estimate the measure of approximation of the initial data, the \(l_1\) metric is used, which has a probabilistic rationale as a maximum likelihood method for two-sided exponential noise distribution. This approximation problem can also be interpreted as an improper (has no solution) interpolation problem, for which it is required to change (correct) optimally the positions of the points so that they all lie on the same hyperplane. In addition, the case of preliminary linear data transformation is considered, while the original information matrix is subject to correction. Therefore, the arising problems belong to the new class of parametric correction. It is shown that these approximation (corrections) problems can be reduced to a set of a finite number of linear programming problems.