Geodesic
On solutions to the equation for improving additives in regression problems
Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 127-146 
Yu. Yu. Linke; A. I. Sakhanenko. On solutions to the equation for improving additives in regression problems. Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 127-146. http://geodesic.mathdoc.fr/item/MT_2011_14_2_a5/
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     title = {On solutions to the equation for improving additives in regression problems},
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     url = {http://geodesic.mathdoc.fr/item/MT_2011_14_2_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article, we consider the problem of finding a solution to a functional equation which in a special way depends on the distribution of a random variable. Such equations naturally arise in construction of consistent estimates in regression problems in the case when the variances of the main observations depend on underlying unknown parameter and the regression coefficients are determined with random errors. A simple example of a regression problem is demonstrated when the equation under consideration occurs.

[1] Gelfand I. M., Shilov G. E., Obobschennye funktsii. Prostranstva osnovnykh i obobschennykh funktsii, Vyp. 2, Fiz.-mat. lit., M., 1958 | MR

[2] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[3] Linke Yu. Yu., Sakhanenko A. I., “Asimptoticheski optimalnoe otsenivanie v zadache lineinoi regressii pri nevypolnenii nekotorykh klassicheskikh predpolozhenii”, Sib. matem. zhurn., 50:2 (2009), 380–396 | MR

[4] Sakhanenko A. I., Linke Yu. Yu., “Asimptoticheski optimalnoe otsenivanie v zadache drobno-lineinoi regressii so sluchainymi oshibkami v koeffitsientakh”, Sib. matem. zhurn., 47:6 (2006), 1372–1400 | MR | Zbl

[5] Sakhanenko A. I., Linke Yu. Yu., “Uluchshenie otsenok v zadache lineinoi regressii so sluchainymi oshibkami v koeffitsientakh”, Sib. matem. zhurn., 52:1 (2011), 143–160 | MR | Zbl

[6] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984 | Zbl

[7] Shilov G. E., Matematicheskii analiz. Vtoroi spetsialnyi kurs, Nauka, M., 1965 | MR