Geodesic
On solutions to the equation for improving additives in regression problems
Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 127-146.

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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. 
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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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