Matrix rank/inertia formulas for least-squares solutions with statistical applications

• Autorzy: Yongge Tian , Bo Jiang
• Języki publikacji: EN

Abstrakty

EN

Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function Φ(Z) = Q − ZPZ0 is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this paper, we establish a group of formulas for calculating maximum and minimum ranks and inertias of Φ(Z) subject to the LSS of AZ = B, and derive many quadratic matrix equalities and inequalities for LSSs from the rank and inertia formulas. This work is motivated by some inference problems on OLSEs under general linear models, while the results obtained can be applied to characterize many algebraical and statistical properties of the OLSEs.

Słowa kluczowe

EN

Linear model; matrix equation; LSS; OLSE; quadratic matrix-valued function; rank, inertia

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 130-140

Daty

otrzymano

2015-06-11

zaakceptowano

2016-02-01

online

2016-02-12

Twórcy

autor

Yongge Tian

• China Economics and Management Academy, Central University of Finance and Economics, Beijing, China

autor

Bo Jiang

• College of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai, China

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Identyfikatory

DOI

10.1515/spma-2016-0013