Publisher: John Wiley and Sons.
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Contents of the book |
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PartOne: Theories |
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Chapter 1.
Robust
Statistics |
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1.1.
Robust
Aspects of Data |
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1.2.
Robust
Statistics and the Mechanism
for Producing Outliers |
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1.3
Location and
Scale
Parameters |
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1.3.1
Location Parameter |
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1.3.2
Scale Parameters |
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1.3.3
Location and Dispersion
Models |
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1.3.4
Numerical Computation of M-estimates |
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1.4
Redescending M-Estimates |
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1.5.
Breakdown
Point |
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1.6.
Linear regression |
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1.7
Robust
Approach in Linear Regression |
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1.8 S-Estimate |
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1.9
Least Absolute and Quantile Esimates |
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1.10
Outlier Detection in Linear Regression |
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1.10.1
Studentized and Deletion Studentized Residuals |
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1.10.2
Hadi Potential |
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1.10.3
Elliptic Norm (Cook
Distance) |
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1.10.4
Difference in
Fits |
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1.10.5
Atkinson’s Distance |
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1.10.6
DFBETAS |
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Chapter 2. Nonlinear models |
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2.1.Introduction to nonlinear modelling. |
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2.2. Least Square (and inferences) |
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2.3.Generalized Least Square (and inferences) |
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2.4.MLE (and inferences) |
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2.5.M and MM estimates (and inferences) |
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2.6.Generalized M estimate (and inferences) |
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2.7.Robust Nonlinear Modelling approach. |
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2.8.Preliminary test estimation. |
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2.9 t-distribution assumption for error terms. (t-regression) optional |
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Chapter 3.
Heteroscedastic variance |
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Non constant variance problem will be discussed in this chapter. In each method,
three different cases will be discussed. |
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3.1.Introduction to Variance heterogeneity |
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3.1.1. Case 1: Numerical
values as the weights |
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3.1.2. Case 2; Variance
model as a parametric function of predictors. |
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3.1.3. Case 3: Variance
model as a parametric function of nonlinear model function. |
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3.2.Weighted estimates |
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3.3.Generalized Least Square |
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3.4.MLE's |
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3.5.Chi square based estimate |
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3.6.Quasi likelihood |
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3.7.Multi stage estimate |
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3.9.Inferences. |
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Chapter 4.
Authocorelated errors |
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This chapter will handle the autocorelated error cases such as AR and ARIMA.
Classic and Robust methods will be explained, such as two stage estimates. |
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4.1 AR |
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4.2 ARIMA |
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Chapter 5. Outlier
Detection. |
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This chapter will discuss about how to detect outliers, statistics measure of
outlier detection will be explained and will be shown how extend from linear to
nonlinear and how should be combined with robust methods; new methods in outlier
detection will be presented and illustrated with real-life data. |
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5.1. Tangential Leverages. |
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5.2.Jacobian Leverages. |
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5.3.Robust Jacobian Leverage. |
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5.4.Introducing outlier detection Measures |
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5.5.New Outlier detection measures. |
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5.6. Outlier detection for authocorrelated error case |
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5.7.Outlier detection for heteroscedastic error case |
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Chapter 6. Nonlinear
Mixed Models, Classic and Robust. |
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In this chapter new robustified methods for nonlinear mixed models will be
explained. |
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6.1. Two Stage estimate |
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6.2.Robust two stage estimate |
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6.3. Application in longitudinal data, (optional, just if can develop methods or
find enough materials) |
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Chapter 7.
Optimization. |
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7.1.Derivative based methods |
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7.2.Derivative free methods |
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Chapter 8. R packages
in Nonlinear regression. |
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In this chapter available packages of R in nonlinear regression and Robust will
be explained. |
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8.1."nlreg" package |
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8.2. “nlr” function |
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8.3. "robustbase" package |
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Chapter 9. A New R
package in Robust Nonlinear Regression. |
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In this chapter a new R package will be proposed. |
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9.1. Nonlinear Objects |
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8.2. Fitting classic and robust models |
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8.3. Heteroscedastic error. |
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8.4. Autocorrelated errors. |
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8.5. Outlier Detection. |
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8.6. Nonlinear Statistical Inference. |
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8.7. Package Comparisons. |
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8.8. Advance Nonlinear Object Programing |
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8.8.1 Defining New
Likelihood Function |
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8.8.2 Fitting
Classic and Robust methods |
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8.8.3
Heteroscedastic error |
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8.8.4 Autocorelated
error |
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8.8.5 Outlier
detection |
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8.9. Robust Nonlinear Mixed models |
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Chapter 10.
Preliminary Discussion in Bayesian Nonlinear regression models. (optional, just
if can develop methods or find enough materials) |
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Robust Bayesian Nonlinear regression models are not well developed. In this
chapter some basics, according to the advances in this field will be explained. |
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10.2.Theories |
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10.2.WinBUGS examples |
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Chapter 11. Neural Network nonlinear regression |
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11.1 Theories |
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11.2 Applications |
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Chapter 12. Genetic algorithm |
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12.1 Theories |
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12.2 Application |
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Apendix A: Mathematics Fundation, in this Appendix the mathematical background
required in the book will be explained, such as Matrix Algebra. |
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Apendix B: Objects |
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In this Section the data set used in the
book, and nonlinear models including, variance functions, robust functions, will
be discussed. |
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B.1 Data Set |
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B.2 Nonlinear Models, illustrating some
nonlinear models. |
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B.3 Variance Function Models |
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B.4 Robust Functions |