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A generalized Fellner-Schall method for smoothing parameter optimization with application to Tweedie location, scale

Simon N Wood1, Matteo Fasiolo1

  • 1School of Mathematics, University of Bristol, Bristol, UK.

Biometrics
|February 14, 2017
PubMed
Summary

This study introduces a generalized Fellner-Schall method for optimizing smoothing parameters and variance components in penalized regression models. The enhanced approach offers computational efficiency and broader applicability for complex statistical modeling.

Keywords:
FisheriesGAMLSSREMLSmoothing parameterSparse additive model

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Area of Science:

  • Statistics
  • Computational Statistics
  • Statistical Modeling

Background:

  • Penalized regression models are widely used for smoothing and regularization.
  • Estimating smoothing parameters and variance components is crucial for model performance.
  • Existing methods like Fellner-Schall have limitations in generality and computational efficiency.

Purpose of the Study:

  • To generalize the Fellner-Schall method for optimizing smoothing parameters and variance components.
  • To extend the method to handle penalties linear in multiple smoothing parameters, including tensor product and adaptive smoothers.
  • To demonstrate the method's convergence properties, relation to Newton optimization, and applicability to Fisher regular likelihoods.

Main Methods:

  • Generalization of the Fellner-Schall algorithm for penalized likelihood models.
  • Extension to handle penalties linear in multiple smoothing parameters.
  • Theoretical analysis of convergence and relation to Newton optimization.
  • Application to Fisher regular likelihoods and various statistical models.

Main Results:

  • The generalized method increases restricted marginal likelihood and converges faster than the EM algorithm.
  • It simplifies parameter estimation by requiring only first and second derivatives of the log-likelihood.
  • Demonstrated successful application to tensor product, adaptive smoothers, Tweedie models, and sparse additive models.
  • Achieved significant computational efficiency gains, particularly in sparse additive modeling.

Conclusions:

  • The generalized Fellner-Schall method provides a computationally efficient and broadly applicable approach for estimating smoothing parameters and variance components.
  • It overcomes limitations of previous methods, enabling analysis of complex models previously considered impractical.
  • The method offers a significant simplification in implementation while maintaining or improving performance.