On best linear unbiased estimation and prediction under a constrained linear random-effects model

Bo Jiang; Yongge Tian

doi:10.3934/jimo.2021209

Article Contents

2023, Volume 19, Issue 2: 852-867. Doi: 10.3934/jimo.2021209

This issue Previous Article Multi-objective optimization of multi-microgrid power dispatch under uncertainties using interval optimization Next Article A novel algorithm for approximating common solution of a system of monotone inclusion problems and common fixed point problem

On best linear unbiased estimation and prediction under a constrained linear random-effects model

Bo Jiang^a, and
Yongge Tian^b, ,

a.
College of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai, Shandong, China
b.
College of Business and Economics, Shanghai Business School, Shanghai, China

^* Corresponding author
^* Corresponding author

Received: April 30, 2021

Revised: August 31, 2021

Early access: December 2021

Published: February 2023

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Abstract

This paper is concerned with solving some fundamental estimation, prediction, and inference problems on a linear random-effects model with its parameter vector satisfying certain exact linear restrictions. Our work includes deriving analytical formulas for calculating the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) of all unknown parameters in the model by way of solving certain constrained quadratic matrix optimization problems, characterizing various mathematical and statistical properties of the predictors and estimators, establishing various fundamental rank and inertia formulas associated with the covariance matrices of predictors and estimators, and presenting necessary and sufficient conditions for several equalities and inequalities of covariance matrices of the predictors and estimators to hold.

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Mathematics Subject Classification: Primary: 62F10; Secondary: 62F30, 62J05.

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