The weight coefficients in the weighted least squares method
Igor Vicheslavovich Bychkov1, Valery lvanovich Zorkaltsev2, Anna Vasilevna Kazazaeva3
1Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Lermontov St., 134, Irkutsk, 664033, Russia
2Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Lermontov St., 130, Irkutsk,664033, Russia
3Irkutsk State University, Karl Marx St., 1, Irkutsk, 664003, Russia
Keywords: mathematical model, agreement of parameters, the least squares method, weight coefficients
Abstract
We consider the problem of estimating parameters of linear mathematical models. It is proved that due to the choice of weights in the least squares method it is possible to obtain solutions by minimizing any penalty functions of a wide class, including those of the Holder norms. A limitation on a set of solutions resulting from the variation of the weights in the least squares method has been determined. The possibility of the practical use of the established theoretical facts is illustrated by the ecology-mathematical models.
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