Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules

Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density sub...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Journal of the American Statistical Association Ročník 109; číslo 506; s. 674 - 685
Hlavní autoři:	Koenker, Roger, Mizera, Ivan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Alexandria Taylor & Francis 01.06.2014 Taylor & Francis Group, LLC Taylor & Francis Ltd
Témata:	Algorithms Baseball Bayes estimators Bayes rule Bayesian analysis Bernoulli Hypothesis Constraints Convex analysis Density estimation Empirical Bayes Estimating techniques Estimation methods Estimators Interior points Iterative solutions Kiefer-Wolfowitz maximum likelihood estimator Maximum likelihood estimation Mixture models Mixtures Normal distribution Objective functions Optimization prediction Rules Scientific method Statistics system optimization Theory and Methods
ISSN:	1537-274X, 0162-1459, 1537-274X
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting Bayes rule. The second, motivated by Jiang and Zhang, proposes a new approach to computing the Kiefer–Wolfowitz nonparametric maximum likelihood estimator for mixtures. In contrast to prior methods for these problems, our new approaches are cast as convex optimization problems that can be efficiently solved by modern interior point methods. In particular, we show that the reformulation of the Kiefer–Wolfowitz estimator as a convex optimization problem reduces the computational effort by several orders of magnitude for typical problems , by comparison to prior EM-algorithm based methods, and thus greatly expands the practical applicability of the resulting methods. Our new procedures are compared with several existing empirical Bayes methods in simulations employing the well-established design of Johnstone and Silverman. Some further comparisons are made based on prediction of baseball batting averages. A Bernoulli mixture application is briefly considered in the penultimate section.
Bibliografie:	http://dx.doi.org/10.1080/01621459.2013.869224 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ISSN:	1537-274X 0162-1459 1537-274X
DOI:	10.1080/01621459.2013.869224