Journal ArticleDOI
The Delta Algorithm and GLIM
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A general maximum likelihood algorthm, called the delta algorithm, is introduced, which generalizes Fisher's scoring method and several other existing algorithms, and leads to a general definition of residuals.Abstract:
Summary A general maximum likelihood algorthm, called the delta algorithm, which generalizes Fisher's scoring method and several other existing algorithms, is introduced. The algorithm is derived as a modification of the Newton-Raphson algorithm, and may be interpreted as an iterative weighted least squares method. We show that for certain models, the algorithm may be implemented in GuM, allowing a number of new models to be fitted in GuM. The algorithm is applied to marginal and conditional maximum likelihood estimation, and the relation with the EM algorithm for incomplete data problems is discussed. Finally, the approach leads to a general definition of residuals, which we consider in some detail.read more
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Journal ArticleDOI
Models for exceedances over high thresholds
Anthony C. Davison,Richard Smith +1 more
TL;DR: In this article, the authors discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds, and the natural distribution for such exceedances, the generalized Pareto distribution, is described and its properties elucidated.
Journal ArticleDOI
Iteratively Reweighted Least Squares for Maximum Likelihood Estimation, and Some Robust and Resistant Alternatives
TL;DR: The scope of application of iteratively reweighted least squares to statistical estimation problems is considerably wider than is generally appreciated as mentioned in this paper, and it extends beyond the exponential-family-type generalized linear models to other distributions, to non-linear parameterizations, and to dependent observations.
Journal ArticleDOI
A mixture likelihood approach for generalized linear models
Michel Wedel,Wayne S. DeSarbo +1 more
TL;DR: This work generalizes the McCullagh and Nelder approach to a latent class framework and demonstrates how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature.
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Generalized Logistic Models
TL;DR: In this article, a class of models indexed by two shape parameters is introduced, both to extend the scope of the standard logistic model to asymmetric probability curves and improve the fit in the noncentral probability regions.
Journal ArticleDOI
Dealing with missing data - Part II
Beata Walczak,Desire Massart +1 more
TL;DR: The main concepts of the maximum likelihood approach in dealing with missing data are introduced and simple numerical examples of the application of ML are presented Differences between ML and other techniques of treating missing data.
References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Book
Generalized Linear Models
Peter McCullagh,John A. Nelder +1 more
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Journal ArticleDOI
Generalized Linear Models
TL;DR: In this paper, the authors used iterative weighted linear regression to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation.
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.