Exponential family nonlinear models
This book deals with statistical inference for exponential family nonlinear models. These models are extensions of generalized linear models and normal nonlinear regression models. The author introduces a modified BW geometric framework which is a modification of the approach suggested by \textit{D. M. Bates} and \textit{D. G. Watts} [J. R. Stat. Soc., Ser. B 42, 1-25 (1980; Zbl 0455.62028)] for the study of such models from a geometric point of view. The contents of the book are as follows: Chapter 1: Exponential family ; Chapter 2: Exponential family nonlinear models; Chapter 3: Geometric framework; Chapter 4: Some second order asymptotics; Chapter 5: Confidence regions; Chapter 6: Diagnostics and influence analysis; Chapter 7: Extension; Appendices: A. Matrix and array; B. Some asymptotic results; Bibliography. The first two chapters discuss statistical properties of exponential families and exponential families of nonlinear models. The last chapter extends some material in the first few chapters, such as curved exponential families, multinomial nonlinear models, etc. The book is well written. It contains detailed proofs of various results discussed in the book with a sprinkling of examples. However, it is mostly theoretical in nature and should be of great interest for researchers working in the area of nonlinear regression.
scientific article; zbMATH DE number 1219606