Robust Nonlinear Regression

Robust Nonlinear Regression

by Hossein Riazoshams, Habshah Midi, Gebrenegus Ghilagaber
Released August 2018
Publisher(s): Wiley
ISBN: 9781118738061

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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 S-language 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
Robust Nonlinear Regression: with Applications using R is an ideal text for statisticians, biostatisticians, and statistical consultants, as well as advanced level students of statistics.

Table of contents

  1. Cover
  2. Dedication
  3. Preface
  4. Acknowledgements
  5. About the Companion Website
  6. Part One: Theories
    1. Chapter 1: Robust Statistics and its Application in Linear Regression
      1. 1.1 Robust Aspects of Data
      2. 1.2 Robust Statistics and the Mechanism for Producing Outliers
      3. 1.3 Location and Scale Parameters
      4. 1.4 Redescending M‐estimates
      5. 1.5 Breakdown Point
      6. 1.6 Linear Regression
      7. 1.7 The Robust Approach in Linear Regression
      8. 1.8 S‐estimator
      9. 1.9 Least Absolute and Quantile Esimates
      10. 1.10 Outlier Detection in Linear Regression
    2. Chapter 2: Nonlinear Models: Concepts and Parameter Estimation
      1. 2.1 Introduction
      2. 2.2 Basic Concepts
      3. 2.3 Parameter Estimations
      4. 2.4 A Nonlinear Model Example
    3. Chapter 3: Robust Estimators in Nonlinear Regression
      1. 3.1 Outliers in Nonlinear Regression
      2. 3.2 Breakdown Point in Nonlinear Regression
      3. 3.3 Parameter Estimation
      4. 3.4 Least Absolute and Quantile Estimates
      5. 3.5 Quantile Regression
      6. 3.6 Least Median of Squares
      7. 3.7 Least Trimmed Squares
      8. 3.8 Least Trimmed Differences
      9. 3.9 S‐estimator
      10. 3.10 ‐estimator
      11. 3.11 MM‐estimate
      12. 3.12 Environmental Data Examples
      13. 3.13 Nonlinear Models
      14. 3.14 Carbon Dioxide Data
      15. 3.15 Conclusion
    4. Chapter 4: Heteroscedastic Variance
      1. 4.1 Definitions and Notations
      2. 4.2 Weighted Regression for the Nonparametric Variance Model
      3. 4.3 Maximum Likelihood Estimates
      4. 4.4 Variance Modeling and Estimation
      5. 4.5 Robust Multistage Estimate
      6. 4.6 Least Squares Estimate of Variance Parameters
      7. 4.7 Robust Least Squares Estimate of the Structural Variance Parameter
      8. 4.8 Weighted M‐estimate
      9. 4.9 Chicken‐growth Data Example
      10. 4.10 Toxicology Data Example
      11. 4.11 Evaluation and Comparison of Methods
    5. Chapter 5: Autocorrelated Errors
      1. 5.1 Introduction
      2. 5.2 Nonlinear Autocorrelated Model
      3. 5.3 The Classic Two‐stage Estimator
      4. 5.4 Robust Two‐stage Estimator
      5. 5.5 Economic Data
      6. 5.6 ARIMA(1,0,1)(0,0,1)7 Autocorrelation Function
    6. Chapter 6: Outlier Detection in Nonlinear Regression
      1. 6.1 Introduction
      2. 6.2 Estimation Methods
      3. 6.3 Point Influences
      4. 6.4 Outlier Detection Measures
      5. 6.5 Simulation Study
      6. 6.6 Numerical Example
      7. 6.7 Variance Heteroscedasticity
      8. 6.8 Conclusion
  7. Part Two: Computations
    1. Chapter 7: Optimization
      1. 7.1 Optimization Overview
      2. 7.2 Iterative Methods
      3. 7.3 Wolfe Condition
      4. 7.4 Convergence Criteria
      5. 7.5 Mixed Algorithm
      6. 7.6 Robust M‐estimator
      7. 7.7 The Generalized M‐estimator
      8. 7.8 Some Mathematical Notation
      9. 7.9 Genetic Algorithm
    2. Chapter 8: nlr Package
      1. 8.1 Overview
      2. 8.2 nl.form Object
      3. 8.3 Model Fit by nlr
      4. 8.4 nlr.control
      5. 8.5 Fault Object
      6. 8.6 Ordinary Least Squares
      7. 8.7 Robust Estimators
      8. 8.8 Heteroscedastic Variance Case
      9. 8.9 Autocorrelated Errors
      10. 8.10 Outlier Detection
      11. 8.11 Initial Values and Self‐start
    3. Chapter 9: Robust Nonlinear Regression in R
      1. 9.1 Lakes Data Examples
      2. 9.2 Simulated Data Examples
  8. Appendix A: nlr Database
    1. A.1 Data Set used in the Book
    2. A.2 Nonlinear Regression Models
    3. A.3 Robust Loss Functions Data Bases
    4. A.4 Heterogeneous Variance Models
  9. References
  10. Index
  11. End User License Agreement

Product information

  • Title: Robust Nonlinear Regression
  • Author(s): Hossein Riazoshams, Habshah Midi, Gebrenegus Ghilagaber
  • Release date: August 2018
  • Publisher(s): Wiley
  • ISBN: 9781118738061