Exponential family mixture models (with least-squares estimators)
Reads0
Chats0
TLDR
For an arbitrary one parameter exponential family density, the authors showed how to construct a mixing distribution (prior) on the parameter in such a way that the resulting mixture distribution is a two (or more)parameter exponential family.Abstract:
For an arbitrary one parameter exponential family density it is shown how to construct a mixing distribution (prior) on the parameter in such a way that the resulting mixture distribution is a two (or more) parameter exponential family. Reweighted infinitely divisible distributions are shown to be the parametric mixing distributions for which this occurs. As an illustration conditions are given under which a parametric mixture of negative exponentials is in the exponential family. Properties of the posterior are given, including linearity of the posterior mean in the natural parameter. For the discrete case a class of simply-computed yet fully-efficient least-squares estimators is given. A Poisson example is used to demonstrate the strengths and weaknesses of the approach.read more
Citations
More filters
Journal ArticleDOI
Exponential Dispersion Models
TL;DR: In this paper, les proprietes generales de la classe des modeles de dispersion exponentiels, which est la generalisation multivariable des modele de distribution d'erreur de Nelder et Wedderburn (1972), were examined.
Journal ArticleDOI
Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis
TL;DR: In this paper, the authors show that the finite-mixture model for J dichotomous items having T latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if T ≥ (J + 1)/2.
Journal ArticleDOI
Rcapture: Loglinear Models for Capture-Recapture in R
TL;DR: Rcapture as discussed by the authors is an R package for capture-recapture experiments, which can fit three types of models: Cormack-Jolly-Seber, open population and robust design models.
Journal ArticleDOI
Computer-assisted analysis of mixtures (C.A.MAM): statistical algorithms.
TL;DR: This paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one-parameter family of densities and provides a unifying computeroriented concept for the statistical analysis of unobserved heterogeneity in a univariate sample.
Journal ArticleDOI
Some recent research in the analysis of mixture distributions
TL;DR: In this paper, some recent research in the analysis of mixture distributions has been carried out and some of the results have been published in the journal "Vol. 21, No. 4, pp. 619-641".
References
More filters
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
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
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.
Journal ArticleDOI
Analysis of Categorical Data by Linear Models
TL;DR: The special cases of linear functions and logarithmic functions of the 7rin are developed in detail, and some examples of how the general approach can be used to analyze various types of categorical data are presented.