A semiparametric scale-mixture regression model and predictive recursion maximum likelihood

Abstract

To avoid specification of the error distribution in a regression model, we propose a general nonparametric scale mixture model for the error distribution. For fitting such mixtures, the predictive recursion method is a simple and computationally efficient alternative to existing methods. We define a predictive recursion-based marginal likelihood function, and estimation of the regression parameters proceeds by maximizing this function. A hybrid predictive recursion--EM algorithm is proposed for this purpose. The method's performance is compared with that of existing methods in simulations and real data analyses.

17 pages, 4 figures, 2 tables

References in corpus (6)

• Asymptotics for minimisers of convex processes
• A nonparametric empirical Bayes framework for large-scale multiple testing
• Consistency of a recursive estimate of mixing distributions
• Stochastic Approximation and Newton's Estimate of a Mixing Distribution
• Semiparametric inference in mixture models with predictive recursion marginal likelihood
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Cited by in corpus (4)

• On nonparametric estimation of a mixing density via the predictive recursion algorithm
• Revisiting consistency of a recursive estimator of mixing distributions
• Estimating a mixing distribution on the sphere using predictive recursion
• A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions