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A Tutorial on MM Algorithms
David R. Hunter,Kenneth Lange +1 more
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The principle behind MM algorithms is explained, some methods for constructing them are suggested, and some of their attractive features are discussed.Abstract:
Most problems in frequentist statistics involve optimization of a function such as a likelihood or a sum of squares. EM algorithms are among the most effective algorithms for maximum likelihood estimation because they consistently drive the likelihood uphill by maximizing a simple surrogate function for the log-likelihood. Iterative optimization of a surrogate function as exemplified by an EM algorithm does not necessarily require missing data. Indeed, every EM algorithm is a special case of the more general class of MM optimization algorithms, which typically exploit convexity rather than missing data in majorizing or minorizing an objective function. In our opinion, MM algorithms deserve to be part of the standard toolkit of professional statisticians. This article explains the principle behind MM algorithms, suggests some methods for constructing them, and discusses some of their attractive features. We include numerous examples throughout the article to illustrate the concepts described. In addition t...read more
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References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Book
Applied Logistic Regression
David W. Hosmer,Stanley Lemeshow +1 more
TL;DR: Hosmer and Lemeshow as discussed by the authors provide an accessible introduction to the logistic regression model while incorporating advances of the last decade, including a variety of software packages for the analysis of data sets.
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Applied Logistic Regression.
TL;DR: Applied Logistic Regression, Third Edition provides an easily accessible introduction to the logistic regression model and highlights the power of this model by examining the relationship between a dichotomous outcome and a set of covariables.
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Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
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Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.