@article{Gong2024, 
author = {Li Gong and Bo Jiang},
title = {A matrix analysis of BLMBPs under a general linear model and its transformation},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {1840-1860},
keywords = {general linear model, transformed general linear model, LMBP, BLMBP, relationships, rank},
url = {https://www.sciopen.com/article/10.3934/math.2024090},
doi = {10.3934/math.2024090},
abstract = {This paper is concerned with the relationships between best linear minimum biased predictors (BLMBPs) in the context of a general linear model (GLM) and its transformed general linear models (TGLMs). We shall establish a mathematical procedure by means of some exact and analytical tools in matrix theory that were developed in recent years. The coverage includes constructing a general vector composed of all unknown parameters in the context of a GLM and its TGLMs, deriving the exact expressions of the BLMBPs through the technical use of analytical solutions of a constrained quadratic matrix-valued function optimization problem in the Löwner partial ordering, and discussing a variety of theoretical performances and properties of the BLMBPs. We also give a series of characterizations of relationships between BLMBPs under a given GLM and its TGLMs.}
}