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VOL. 57 | 2009 Mixed Models, Posterior Means and Penalized Least-Squares


This paper reviews the connections between estimators that derive from three different modeling methodologies: Mixed-effects models, Bayesian models and Penalized Least-squares. Extension of classical results on the equivalence for smoothing spline estimators and best linear unbiased prediction and/or posterior analysis of certain Gaussian signal-plus-noise models is examined in a more general setting. These connections allow for the application of an efficient, linear time algorithm, to estimate parameters, compute random effects predictions and evaluate likelihoods in a large class of model scenarios. We also show that the methods of generalized cross-validation, restricted maximum likelihood and unbiased risk prediction can be used to estimate the variance components or adaptively select the smoothing parameters in any of the three settings.


Published: 1 January 2009
First available in Project Euclid: 3 August 2009

zbMATH: 1271.62088
MathSciNet: MR2681665

Digital Object Identifier: 10.1214/09-LNMS5713

Primary: 62J05
Secondary: 65C20

Keywords: adaptive selection , Bayesian prediction , Kalman fiter , p-splines , Ridge regression , smoothing splines , varying coefficient models

Rights: Copyright © 2009, Institute of Mathematical Statistics


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