2-inverses and their statistical application
type: Item
instance of: scholarly article
title: 2-inverses and their statistical application
zbMATH Open document ID: 0671.62003
author: Albert J. Getson
author: Francis C. Hsuan
published in: Lecture Notes in Statistics
publication date: 1988-01-01T00:00:00Z
review text: This monograph is a summary of the research on \(\{\) \(2\}\)-inverses. It provides an in-depth, elegant treatment of generalized inverses and related topics in terms of \(\{\) \(2\}\)-inverses, in a simple mathematical language. It is organized into five chapters beginning with an introduction which contains a detailed outline of the book. Chapter 2 presents a functional approach for constructing generalized inverses which makes \(\{\) \(2\}\)-inverses the focal point. Several specific properties of \(\{\) \(2\}\)-inverses are also given. Chapter 3 is devoted to the study of the role of generalized inverses, especially \(\{\) \(2\}\)-inverses in quadratic forms and second degree polynomials. Chapter 4 gives an excellent treatment of the least squares solution with and without constraints in terms of the Bott-Duffin inverses, a special \(\{\) \(2\}\)-inverse. Chapter 5 demonstrates the role of the Bott-Duffin inverses in providing a consistent theory unifying various approaches for constructing sums of squares in unbalanced linear models. In summary, statisticians and researchers in related scientific fields will find that the book gives some insight into generalized inverses.
reviewed by: Song Wang
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62J99
Mathematics Subject Classification ID: 62-01
Mathematics Subject Classification ID: 62H99
zbMATH DE Number: 4098482
zbMATH Keywords: generalized linear models
zbMATH Keywords: generalized inverses
zbMATH Keywords: functional approach
zbMATH Keywords: quadratic forms
zbMATH Keywords: second degree polynomials
zbMATH Keywords: least squares
zbMATH Keywords: constraints
zbMATH Keywords: Bott-Duffin inverses
zbMATH Keywords: sums of squares
zbMATH Keywords: unbalanced linear models
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4098482