Geodesic
The weight coefficients in the weighted least squares method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 275-288 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 Hölder 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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I. V. Bychkov; V. I. Zorkaltsev; A. V. Kazazaeva. The weight coefficients in the weighted least squares method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 275-288. http://geodesic.mathdoc.fr/item/SJVM_2015_18_3_a2/

[1] Ajvazyan S. A., Prikladnaya statistika: Osnovy modelirovaniya i pervichnaya obrabotka dannykh, Spravochnoe izd-nie, eds. S. A. Ajvazyan, I. S. Enyukov, L. D. Meshalkin, Finansy i statistika, M., 1983 | MR

[2] Gauss K. F., Izbrannye geodezicheskie sochineniya, Geodezizdat, M., 1957

[3] Dikin I. I., Zorkal'tsev V. I., Iterativnoe reshenie zadach matematicheskogo programmirovaniya (algoritmy metoda vnutrennikh tochek), Nauka, Sib. otd-nie, Novosibirsk, 1980 | MR

[4] Eremin I. I., Mazurov V. D., Astakhov N. N., Nesobstvennye zadachi linejnogo i vypuklogo programmirovaniya, Nauka, M., 1983 | MR

[5] Zorkal'tsev V. I., Metod naimen'shikh kvadratov: geometricheskie svojstva, al'ternativnye podkhody, prilozheniya, eds. E. G. Antsiferov, V. P. Bulatov, VO “Nauka”, Sibirskaya izdatel'skaya firma, Novosibirsk, 1995 | MR

[6] Zorkal'tsev V. I., Mokryj I. V., Kazazaeva A. V., “Modelirovanie pelagicheskogo soobshchestva ozera Bajkal”, Vychislitel'nye tekhnologii, 16:1 (2011), 48–66 | MR | Zbl

[7] Kolmogorov A. I., Teoriya veroyatnosti i matematicheskaya statistika, Nauka, M., 1986 | MR

[8] Linnik Yu. V., Metod naimen'shikh kvadratov i osnovy matematiko-statisticheskoj teorii nablyudenij, Fizmatgiz, M., 1962 | MR

[9] Starikov G. V., Golomyanki Bajkala, Nauka, Sib. otd-nie, Novosibirsk, 1977

[10] Chebotarev A. S., Sposob naimen'shikh kvadratov s osnovami teorii veroyatnosti, Geodezizdat, M., 1958 | MR