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

100%

Tian Y., Jiang B.

Special Matrices

2016

tom 4

nr 1

130-140

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.

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Decomposing matrices with Jerzy K. Baksalary

84%

Isotalo J., Puntanen S., Styan G.

Discussiones Mathematicae Probability and Statistics

2008

tom 28

nr 1

91-111

In this paper we comment on some papers written by Jerzy K. Baksalary. In particular, we draw attention to the development process of some specific research ideas and papers now that some time, more than 15 years, has gone after their publication.

Ograniczanie wyników

1 Discussiones Mathematicae Probability and Statistics

1 Special Matrices

1 Isotalo J.

1 Jiang B.

1 Puntanen S.

1 Styan G.

1 Tian Y.

1 2016

1 2008

Wyniki wyszukiwania

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

Decomposing matrices with Jerzy K. Baksalary