Smoothing Parameter and Model Selection for General Smooth Models

This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of model selection tools available. The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where…

• DF
  Deutsche Forschungsgemeinschaft

  Awards: RTG 1644, (DFG)
• AF
  Albert-Ludwigs-Universität Freiburg
• EA
  Engineering and Physical Sciences Research Council

  Awards: EP/K005251/1, EP/I000917/1