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

Simon N. Wood*, Matteo Fasiolo

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

22 Citations (Scopus)
342 Downloads (Pure)

Abstract

We consider the optimization of smoothing parameters and variance components in models with a regular log likelihood subject to quadratic penalization of the model coefficients, via a generalization of the method of Fellner (1986) and Schall (1991). In particular: (i) we generalize the original method to the case of penalties that are linear in several smoothing parameters, thereby covering the important cases of tensor product and adaptive smoothers; (ii) we show why the method’s steps increase the restricted marginal likelihood of the model, that it tends to converge faster than the EM algorithm, or obvious accelerations of this, and investigate its relation to Newton optimization; (iii) we generalize the method to any Fisher regular likelihood. The method represents a considerable simplification over existing methods of estimating smoothing parameters in the context of regular likelihoods, without sacrificing generality: for example, it is only necessary to compute with the same first and second derivatives of the log-likelihood required for coefficient estimation, and not with the third or fourth order derivatives required by alternative approaches. Examples are provided which would have been impossible or impractical with pre-existing Fellner-Schall methods, along with an example of a Tweedie location, scale and shape model which would be a challenge for alternative methods, and a sparse additive modelling example where the method facilitates computational efficiency gains of several orders of magnitude.
Original languageEnglish
Pages (from-to)1071-1081
Number of pages11
JournalBiometrics
Volume73
Issue number4
Early online date13 Feb 2017
DOIs
Publication statusPublished - Dec 2017

Structured keywords

  • Jean Golding

Keywords

  • Fisheries
  • GAMLSS
  • REML
  • Smoothing parameter
  • Sparse additive model

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