2-inverses and their statistical application
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.
scientific article; zbMATH DE number 4098482