Robust Nonlinear Regression

with Applications using R

Inbunden, Engelska, 2018

AvHossein Riazoshams,Habshah Midi,Gebrenegus Ghilagaber,Habshah MIDI

1 169 kr

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The first book to discuss robust aspects of nonlinear regression—with applications using R softwareRobust 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 regressionAddresses some commonly mishandled aspects of modelingR packages for both classical and robust nonlinear regression are presented in detail in the book and on an accompanying websiteRobust Nonlinear Regression: with Applications using R is an ideal text for statisticians, biostatisticians, and statistical consultants, as well as advanced level students of statistics.

Produktinformation

Utgivningsdatum2018-08-10
Mått150 x 229 x 18 mm
Vikt454 g
FormatInbunden
SpråkEngelska
Antal sidor264
FörlagJohn Wiley & Sons Inc
ISBN9781118738061

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Matematisk statistik inom Naturvetenskap och teknik

Hossein Riazoshams, PhD, is a full-time Faculty member at the Department of Mathematics and Statistics, Lamerd Islamic Azad University of Iran; Stockholm University, Sweden; and University of Putra, Malaysia. Habshah Midi, PhD, is Professor at the Department of Mathematics, Faculty of Science and Institute for Mathematical Research, University of Putra, Malaysia. Gebrenegus Ghilagaber, PhD, is Professor and Head at the Department of Statistics, Stockholm University, Sweden.

Preface xiAcknowledgements xiiiAbout the Companion Website xvPart One Theories 11 Robust Statistics and its Application in Linear Regression 31.1 Robust Aspects of Data 31.2 Robust Statistics and the Mechanism for Producing Outliers 41.3 Location and Scale Parameters 51.3.1 Location Parameter 51.3.2 Scale Parameters 91.3.3 Location and Dispersion Models 101.3.4 Numerical Computation of M-estimates 111.4 Redescending M-estimates 131.5 Breakdown Point 131.6 Linear Regression 161.7 The Robust Approach in Linear Regression 191.8 S-estimator 231.9 Least Absolute and Quantile Esimates 251.10 Outlier Detection in Linear Regression 271.10.1 Studentized and Deletion Studentized Residuals 271.10.2 Hadi Potential 281.10.3 Elliptic Norm (Cook Distance) 281.10.4 Difference in Fits 291.10.5 Atkinson’s Distance 291.10.6 DFBETAS 292 NonlinearModels: Concepts and Parameter Estimation 312.1 Introduction 312.2 Basic Concepts 322.3 Parameter Estimations 342.3.1 Maximum Likelihood Estimators 342.3.2 The Ordinary Least Squares Method 362.3.3 Generalized Least Squares Estimate 382.4 A NonlinearModel Example 393 Robust Estimators in Nonlinear Regression 413.1 Outliers in Nonlinear Regression 413.2 Breakdown Point in Nonlinear Regression 433.3 Parameter Estimation 443.4 Least Absolute and Quantile Estimates 443.5 Quantile Regression 453.6 Least Median of Squares 453.7 Least Trimmed Squares 473.8 Least Trimmed Differences 483.9 S-estimator 493.10 ��-estimator 503.11 MM-estimate 503.12 Environmental Data Examples 533.13 NonlinearModels 553.14 Carbon Dioxide Data 613.15 Conclusion 644 Heteroscedastic Variance 674.1 Definitions and Notations 694.2 Weighted Regression for the Nonparametric Variance Model 694.3 Maximum Likelihood Estimates 714.4 VarianceModeling and Estimation 724.5 Robust Multistage Estimate 744.6 Least Squares Estimate of Variance Parameters 754.7 Robust Least Squares Estimate of the Structural Variance Parameter 784.8 Weighted M-estimate 794.9 Chicken-growth Data Example 804.10 Toxicology Data Example 854.11 Evaluation and Comparison of Methods 875 Autocorrelated Errors 895.1 Introduction 895.2 Nonlinear Autocorrelated Model 905.3 The Classic Two-stage Estimator 915.4 Robust Two-stage Estimator 925.5 Economic Data 935.6 ARIMA(1,0,1)(0,0,1)7 Autocorrelation Function 1036 Outlier Detection in Nonlinear Regression 1076.1 Introduction 1076.2 Estimation Methods 1086.3 Point Influences 1096.3.1 Tangential Plan Leverage 1106.3.2 Jacobian Leverage 1116.3.3 Generalized and Jacobian Leverages for M-estimator 1126.4 Outlier DetectionMeasures 1156.4.1 Studentized and Deletion Studentized Residuals 1166.4.2 Hadi’s Potential 1176.4.3 Elliptic Norm (Cook Distance) 1176.4.4 Difference in Fits 1186.4.5 Atkinson’s Distance 1186.4.6 DFBETAS 1186.4.7 Measures Based on Jacobian and MM-estimators 1196.4.8 Robust Jacobian Leverage and Local Influences 1196.4.9 Overview 1216.5 Simulation Study 1226.6 Numerical Example 1286.7 Variance Heteroscedasticity 1346.7.1 Heteroscedastic Variance Studentized Residual 1366.7.2 Simulation Study, Heteroscedastic Variance 1406.8 Conclusion 141Part Two Computations 1437 Optimization 1457.1 Optimization Overview 1457.2 Iterative Methods 1467.3 Wolfe Condition 1487.4 Convergence Criteria 1497.5 Mixed Algorithm 1507.6 Robust M-estimator 1507.7 The Generalized M-estimator 1517.8 Some Mathematical Notation 1517.9 Genetic Algorithm 1528 nlr Package 1538.1 Overview 1538.2 nl.form Object 1548.2.1 selfStart Initial Values 1598.3 Model Fit by nlr 1618.3.1 Output Objects, nl.fitt 1648.3.2 Output Objects, nl.fitt.gn 1678.3.3 Output Objects, nl.fitt.rob 1698.3.4 Output Objects, nl.fitt.rgn 1698.4 nlr.control 1708.5 Fault Object 1728.6 Ordinary Least Squares 1728.7 Robust Estimators 1758.8 Heteroscedastic Variance Case 1798.8.1 Chicken-growth Data Example 1798.8.2 National Toxicology Study Program Data 1838.9 Autocorrelated Errors 1848.10 Outlier Detection 1938.11 Initial Values and Self-start 2019 Robust Nonlinear Regression in R 2079.1 Lakes Data Examples 2079.2 Simulated Data Examples 211A nlr Database 215A.1 Data Set used in the Book 215A.1.1 Chicken-growth Data 216A.1.2 Environmental Data 216A.1.3 Lakes Data 218A.1.4 Economic Data 221A.1.5 National Texicology Program(NTP) Data 223A.1.6 CowMilk Data 223A.1.7 Simulated Outliers 225A.1.8 Artificially Contaminated Data 227A.2 Nonlinear Regression Models 227A.3 Robust Loss FunctionsData Bases 229A.4 Heterogeneous Variance Models 229References 233Index 239