Nonlinear estimation (Q1188879)

This is a well written book on nonlinear estimation suitable for a wide variety of readers. It has seven chapters, a glossary of unfamiliar terms, a list of references, an author index, and a subject index. The first chapter is an introductory chapter in which the concept of models, parameters, maximum likelihood estimation, and alternative methods of estimation are reviewed. Chapter 2 is a key chapter in which transformations of parameters are discussed in detail. Parameters are classified into three different types: defining parameters, computing parameters, and interpretable parameters. A set of desirable properties for a transformation to have are listed. The concept of stable parameters is introduced and methods for finding them are outlined. Chapter 3 discusses the existence and uniqueness of maximum likelihood solutions for nonlinear problems. Several simple cases are examined in detail, both graphically and analytically, for illustrative purposes. Approximate inference procedures for functions of parameters are outlined. The nonlinear design problem is introduced. Chapter 4 consists of a variety of graphical methods that may be useful in nonlinear modeling situations. A discussion of the computational aspects related to the fitting of nonlinear models is given in chapter 5. Chapter 6 is a short chapter consisting of a description of a few practical applications. Chapter 7, which is the final chapter, gives a description of the Maximum Likelihood Program (MLP) [see the author, Maximum Likelihood Program. Num. Algorithms Group, Oxford (1987)], its capabilities, and some computational details. This book should serve as a very useful reference for statisticians as well as practitioners interested in nonlinear modeling.