Nonlinear EstimationSpringer Science & Business Media, 6 déc. 2012 - 189 pages 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. |
Table des matières
CHAPTER | 12 |
CHAPTER 5 | 32 |
CHAPTER 3 | 44 |
CHAPTER 4 | 73 |
Computing Methods for Nonlinear Modeling | 108 |
CHAPTER 6 | 134 |
CHAPTER 7 | 143 |
APPENDIX | 174 |
| 183 | |
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Expressions et termes fréquents
algorithm analysis approximate asymptote binomial distribution common estimate loci computed confidence intervals confidence limits confidence regions convergence corresponding critical contour curvature curve fitting data points data sets data values defining parameters deviance residuals dispersion matrix equally spaced equations error distribution example expected exponential curve fitted values function of parameters gamma distribution Gauss-Newton method given Gompertz curve initial estimates iterations likelihood contours likelihood function linear parameters linear regression log-likelihood logistic curve lognormal maximum likelihood estimates method minimum model E(y negative binomial negative binomial distribution nonlinear models nonlinear parameters normal errors normally distributed observations obtained optimization orthogonal polynomial parameter estimates parameter loci parameter space plotted Poisson distribution polynomial pseudomodels quadratic range rectangular hyperbola residual sum Royal Statistical Society sample Section solution locus solution region stable ordinates stable parameters Statistical sum of squares three-parameter tion variables variance y₁ zero Φι