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.
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algorithm analysis applied appropriate approximate assumed asymptote becomes binomial close common computed confidence constant contour convergence correlations corresponding critical curve data sets defined depends derivatives described deviance residuals discussed dispersion matrix distribution effect equally equations errors estimates exact example exist expected exponential exponential curve expressed fitted formula function given gives hyperbola illustrated independent initial intervals iterations known likelihood limits linear loci log-likelihood logistic matrix maximum mean method negative nonlinear normal observations obtained optimization origin particular plotted points Poisson polynomial positive possible practical predicted problem procedure quadratic range ratios region regression relationship represents residuals respect roots sample scale shape showing similar single slope solution solution locus solve space stable parameters standard statistics sum of squares Table tends tion transformation unique usually values variables variance weighted zero