Simultaneous optimal predictions under two seemingly unrelated linear random-effects models

Yongge Tian; Pengyang Xie

doi:10.3934/jimo.2020168

Article Contents

2022, Volume 18, Issue 1: 561-573. Doi: 10.3934/jimo.2020168

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Simultaneous optimal predictions under two seemingly unrelated linear random-effects models

Yongge Tian^, and
Pengyang Xie

College of Business and Economics, Shanghai Business School, Shanghai, China

^* Corresponding author: Yongge Tian
^* Corresponding author: Yongge Tian

Received: May 2020

Revised: September 2020

Early access: November 12, 2020

Published online: November 12, 2020

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Abstract

This paper considers simultaneous optimal prediction and estimation problems in the context of linear random-effects models. Assume a pair of seemingly unrelated linear random-effects models (SULREMs) with the random-effects and the error terms correlated. Our aim is to find analytical formulas for calculating best linear unbiased predictors (BLUPs) of all unknown parameters in the two models by means of solving a constrained quadratic matrix optimization problem in the Löwner sense. We also present a variety of theoretical and statistical properties of the BLUPs under the two models.

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Mathematics Subject Classification: Primary: 62F10, 62J05; Secondary: 90C22, 90C90.

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