Nonlinear Estimation

1. Front Matter

   Pages i-viii

   PDF

2. Models, Parameters, and Estimation

   • Gavin J. S. Ross

   Pages 1-11

3. Transformations of Parameters

   • Gavin J. S. Ross

   Pages 12-43

4. Inference and Stable Transformations

   • Gavin J. S. Ross

   Pages 44-72

5. The Geometry of Nonlinear Inference

   • Gavin J. S. Ross

   Pages 73-107

6. Computing Methods for Nonlinear Modeling

   • Gavin J. S. Ross

   Pages 108-133

7. Practical Applications of Nonlinear Modeling

   • Gavin J. S. Ross

   Pages 134-142

8. A Program for Fitting Nonlinear Models, MLP

   • Gavin J. S. Ross

   Pages 143-173

9. Back Matter

   Pages 174-189

   PDF

Non-Linear Estimation is a handbook for the practical statistician or modeller interested in fitting and interpreting non-linear models with the aid of a computer. A major theme of the book is the use of 'stable parameter systems'; these provide rapid convergence of optimization algorithms, more reliable dispersion matrices and confidence regions for parameters, and easier comparison of rival models. The book provides insights into why some models are difficult to fit, how to combine fits over different data sets, how to improve data collection to reduce prediction variance, and how to program particular models to handle a full range of data sets. The book combines an algebraic, a geometric and a computational approach, and is illustrated with practical examples. A final chapter shows how this approach is implemented in the author's Maximum Likelihood Program, MLP.

• Curve fitting
• Fitting
• Likelihood
• Variance
• algorithms
• linear optimization
• optimization

"The novel part of this book is a central theme on the important differences in specific parts of the problem... It contains many interesting ideas, particularly with regard to parameterizations and graphics... people with the relevant type of data should find careful study of this book very rewarding."
(Journal of the Am. Statistical Assoc.)

• Statistics Department, Institute of Arable Crops Research Rothamsted Experimental Station, Harpenden, Herts, England

  Gavin J. S. Ross

Policies and ethics