Ukr. Mat. Zh. - 2015. - 67, № 1. - pp. 128-134
There are some discussions concerning the admissibility of estimated regression coefficients under the balanced loss function in the general linear model. We study this issue for the generalized linear regression model. First, we propose a generalized weighted balance loss function for the generalized linear model. For the proposed loss function, we study sufficient and necessary conditions for the admissibility of the estimated regression coefficients in two interesting linear estimation classes.
Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 63–70
A subgroup H is called nearly ℳ-supplemented in a finite group G if there exists a normal subgroup K of G such that HK ⊴ G and TK < HK for every maximal subgroup T of H. We obtain some new results on supersoluble groups and their formation by using nearly ℳ-supplemented subgroups and study the structure of finite groups.