Nonlinear Regression, Functional Relations and Robust Methods

This book, the second volume in a three part work, provides a comprehensive and unified account of nonlinear regression analysis, functional and structural relations, and of nonparametric and robust estimators. Research in these areas has been stimulated by the increase in computational capabilities and this volume will therefore be of great interest to researchers in statistics as well as applied statisticians working in industry. The material provided includes recent work from German and Russian sources, as well as from English-speaking sources, and the treatment throughout is mathematically rigorous but accessible. The text will benefit rsearchers in statistics and applied statisticians working in industry.

Part of a three-volume set, this monograph surveys the state of the art in research and applications of nonlinear regression, models with errors in the variables, and robust regression analysis, methods which are essential for analyzing experimental data, for modelling, and for investigating cause-and-effect relationships. Incorporating recent work from German and Russian sources, it offers the first comprehensive, unified presentation of the mathematical tools and results in a mathematically rigorous yet readable fashion. Coverage includes estimation, confidence, regions and tests; asymptotic properties such as consistency, normality, and efficiency for maximum likelihood; estimators based on rank and order statistics; and numerical methods for the calulation of estimates. Mathematical results are included in an appendix.