Geodesic
On solutions to the equation for improving additives in regression problems
Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 127-146 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MT_2011_14_2_a5,
     author = {Yu. Yu. Linke and A. I. Sakhanenko},
     title = {On solutions to the equation for improving additives in regression problems},
     journal = {Matemati\v{c}eskie trudy},
     pages = {127--146},
     year = {2011},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2011_14_2_a5/}
}
TY  - JOUR
AU  - Yu. Yu. Linke
AU  - A. I. Sakhanenko
TI  - On solutions to the equation for improving additives in regression problems
JO  - Matematičeskie trudy
PY  - 2011
SP  - 127
EP  - 146
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MT_2011_14_2_a5/
LA  - ru
ID  - MT_2011_14_2_a5
ER  - 
%0 Journal Article
%A Yu. Yu. Linke
%A A. I. Sakhanenko
%T On solutions to the equation for improving additives in regression problems
%J Matematičeskie trudy
%D 2011
%P 127-146
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/MT_2011_14_2_a5/
%G ru
%F MT_2011_14_2_a5
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/

[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