@article{Tian2023, 
author = {Yongge Tian},
title = {An effective treatment of adding-up restrictions in the inference of a general linear model},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {15189-15200},
keywords = {adding-up restrictions, BLUE, estimability, general linear model, OLSE},
url = {https://www.sciopen.com/article/10.3934/math.2023775},
doi = {10.3934/math.2023775},
abstract = {This article offers a general procedure of carrying out estimation and inference under a linear statistical model        y    =      X              β              β    +            ε              ε   with an adding-up restriction        A        y    =      b   to the observed random vector        y  . We first propose an available way of converting the adding-up restrictions to a linear matrix equation for              β              β   and a matrix equality for the covariance matrix of the error term              ε              ε  , which can help in combining the two model equations in certain consistent form. We then give the derivations and presentations of analytic expressions of the ordinary least-squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of parametric vector        K              β              β   using various analytical algebraic operations of the given vectors and matrices in the model.}
}