Book description
The first book to discuss robust aspects of nonlinear regression—with applications using R software
Robust Nonlinear Regression: with Applications using R covers a variety of theories and applications of nonlinear robust regression. It discusses both parts of the classic and robust aspects of nonlinear regression and focuses on outlier effects. It develops new methods in robust nonlinear regression and implements a set of objects and functions in Slanguage under SPLUS and R software. The software covers a wide range of robust nonlinear fitting and inferences, and is designed to provide facilities for computer users to define their own nonlinear models as an object, and fit models using classic and robust methods as well as detect outliers. The implemented objects and functions can be applied by practitioners as well as researchers.
The book offers comprehensive coverage of the subject in 9 chapters: Theories of Nonlinear Regression and Inference; Introduction to R; Optimization; Theories of Robust Nonlinear Methods; Robust and Classical Nonlinear Regression with Autocorrelated and Heteroscedastic errors; Outlier Detection; R Packages in Nonlinear Regression; A New R Package in Robust Nonlinear Regression; and Object Sets.
 The first comprehensive coverage of this field covers a variety of both theoretical and applied topics surrounding robust nonlinear regression
 Addresses some commonly mishandled aspects of modeling
 R packages for both classical and robust nonlinear regression are presented in detail in the book and on an accompanying website
Table of contents
 Cover
 Dedication
 Preface
 Acknowledgements
 About the Companion Website

Part One: Theories

Chapter 1: Robust Statistics and its Application in Linear Regression
 1.1 Robust Aspects of Data
 1.2 Robust Statistics and the Mechanism for Producing Outliers
 1.3 Location and Scale Parameters
 1.4 Redescending M‐estimates
 1.5 Breakdown Point
 1.6 Linear Regression
 1.7 The Robust Approach in Linear Regression
 1.8 S‐estimator
 1.9 Least Absolute and Quantile Esimates
 1.10 Outlier Detection in Linear Regression
 Chapter 2: Nonlinear Models: Concepts and Parameter Estimation

Chapter 3: Robust Estimators in Nonlinear Regression
 3.1 Outliers in Nonlinear Regression
 3.2 Breakdown Point in Nonlinear Regression
 3.3 Parameter Estimation
 3.4 Least Absolute and Quantile Estimates
 3.5 Quantile Regression
 3.6 Least Median of Squares
 3.7 Least Trimmed Squares
 3.8 Least Trimmed Differences
 3.9 S‐estimator
 3.10 ‐estimator
 3.11 MM‐estimate
 3.12 Environmental Data Examples
 3.13 Nonlinear Models
 3.14 Carbon Dioxide Data
 3.15 Conclusion

Chapter 4: Heteroscedastic Variance
 4.1 Definitions and Notations
 4.2 Weighted Regression for the Nonparametric Variance Model
 4.3 Maximum Likelihood Estimates
 4.4 Variance Modeling and Estimation
 4.5 Robust Multistage Estimate
 4.6 Least Squares Estimate of Variance Parameters
 4.7 Robust Least Squares Estimate of the Structural Variance Parameter
 4.8 Weighted M‐estimate
 4.9 Chicken‐growth Data Example
 4.10 Toxicology Data Example
 4.11 Evaluation and Comparison of Methods
 Chapter 5: Autocorrelated Errors
 Chapter 6: Outlier Detection in Nonlinear Regression

Chapter 1: Robust Statistics and its Application in Linear Regression
 Part Two: Computations
 Appendix A: nlr Database
 References
 Index
 End User License Agreement
Product information
 Title: Robust Nonlinear Regression
 Author(s):
 Release date: August 2018
 Publisher(s): Wiley
 ISBN: 9781118738061
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