Total Problem of Constructing Linear Regression Using Matrix Correction Methods with Minimax Criterion - Gorelik, Victor; Zolotova, Tatiana (Mathematics (Basel), 2023)
A linear problem of regression analysis is considered under the assumption of the presence of noise in the output and input variables. This approximation problem may be interpreted as an improper interpolation problem, for which it is required to correct optimally the positions of the original points in the data space so that they all lie on the same hyperplane. The use of the quadratic approximation criterion for such a problem led to the appearance of the total least squares method. In this paper, we use the minimax criterion to estimate the measure of correction of the initial data. It leads to a nonlinear mathematical programming problem. It is shown that this problem can be reduced to solving a finite number of linear programming problems. However, this number depends exponentially on the number of parameters. Some methods for overcoming this complexity of the problem are proposed.