Journal ArticleDOI
The efficient use of function minimization in non-linear maximum-likelihood estimation
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TLDR
Applications to well‐known problems of distribution fitting, quantal responses and least‐squares curve fitting, and sequential minimization and nested minimization can be used to solve particular problems are described.Abstract:
Maximum‐likelihood estimation problems can be solved numerically using function minimization algorithms, but the amount of computing required and the accuracy of the results depend on the way the algorithms are used. Attention to the analytical properties of the model, to the relationship between the model and the data, and to descriptive properties of the data can greatly simplify the problem, sometimes providing a method of solution on a desk calculator. This paper describes how parameter transformation, sequential minimization and nested minimization can be used to solve particular problems. Applications to well‐known problems of distribution fitting, quantal responses and least‐squares curve fitting are described. The implications for computer programming are discussed.read more
Citations
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Journal ArticleDOI
Parameter Orthogonality and Approximate Conditional Inference
David Cox,Nancy Reid +1 more
TL;DR: In this paper, the authors propose a statisticalique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations, and donne les estimateurs du maximum de VRAISEMblance for les parametres de nuisance.
Book
Nonlinear Statistical Models
TL;DR: In this article, a Unified Asymptotic Theory for Nonlinear Regression with Regression Structure (UATRS) is proposed. But it is not a unified theory for dynamic nonlinear models.
Journal ArticleDOI
Akaike's information criterion and recent developments in information complexity
TL;DR: This paper presents some recent developments on a new entropic or information complexity (ICOMP) criterion of Bozdogan for model selection and operationalizes the general form of ICOMP based on the quantification of the concept of overall model complexity in terms of the estimated inverse-Fisher information matrix.
Journal ArticleDOI
The density-dependence of spatial behaviour and the rarity of randomness
TL;DR: Spatial disposition is thus density-dependent and it is deduced that spatial behaviour is also density- dependent as required by Taylor & Taylor's A-model for intrinsic population control by movement.
References
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Journal ArticleDOI
A Rapidly Convergent Descent Method for Minimization
Roger Fletcher,M. J. D. Powell +1 more
TL;DR: A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations.
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An efficient method for finding the minimum of a function of several variables without calculating derivatives
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An Automatic Method for Finding the Greatest or Least Value of a Function
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Contributions to the Mathematical Theory of Evolution
TL;DR: In this paper, the authors discuss the dissection of abnormal frequency-curve into normal curves, which is a special case of the normal curve problem, and the equations for dissection into n normal curves can be written down in the same manner as for the case of n = 2.