Statistical inference under order restrictions
de Richard E. Barlow, H. D. Brunk, J. M. Bremner
The general class of problems explored here are those of estimation and testing when the parameters or characteristics of a model are, a priori, constrained to lie in a region defined by order restrictions among them. That the book is subtitled, "The Theory and Application of Isotonic Regression" is appropriate; the implication being that most of the methods solving these problems involve statistics derived from the statistics natural for the unconstrained model, by means of an isotonic regression function. There have been extensive developments in this area over the past 20 years, many of them by the authors, scattered widely over the journals and these are here collected together in a single source. There are seven chapters. The first two deal with the general problems and applications of estimates of isotonic regression. Chapters 3 and 4 carry this over into a hypothesis testing framework, by a consideration of its use in testing the equality of ordered means, while Chapters 5 and 6 are concerned with estimation and goodness of fit problems of distributions. Chapter 7 is a little out of step with the general approach of the rest of the book. It is an abstract development of theory in measure-theoretic terms, and to anybody but the "purest", certainly to those interested in the book for its methodological emphasis, would perhaps prove unnerving.
