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/...

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Bibliographic Details
Published inLecture notes-monograph series Vol. 57; pp. 216 - 236
Main Author Maldonado, Yolanda Muñoz
Format Journal Article
LanguageEnglish
Published Institute of Mathematical Statistics 01.01.2009
Subjects
Bayesian networks
Coefficients
Confidence interval
Data smoothing
Estimation methods
Estimators
Kalman filters
Matrices
Maximum likelihood estimation
Modeling
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Summary: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.
ISSN:0749-2170
2328-3874