Smoothing Parameter and Model Selection for General Smooth Models

Dados Bibliográficos

ID23345573
AutoresSimon N Wood (0000-0002-2034-7453, University of Bristol, autor correspondente), Natalya Pya (School of Science and Technology, Nazarbayev University, Astana, Kazakhstan, and KIMEP University, Almaty, Kazakhstan), Benjamin Säfken (0000-0003-4702-3333, Chairs of Statistics and Econometrics, Georg-August-Universität Göttingen, Germany)
Ano2016
Volume111
Fascículo516
Páginas1548-1563
Data de publicação2016-10-01
Peer ReviewedSim
Open AccessSim
TipoARTICLE
PeriódicoJournal of the American Statistical Association (JOURNAL)
Identificadores do periódicoISSN: 0162-1459 • E-ISSN: 1537-274X
EditoraInforma UK Limited (PUBLISHER • GB)
DOI10.1080/01621459.2016.1180986
OpenAlexW2593643174
IdiomaEN
Citações recebidas68
Referências citadas35

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 the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for nonexponential family responses (e.g., beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (e.g., two stage zero inflation models, and Gaussian location-scale models), Cox proportional hazards models and multivariate additive models. The framework reduces the implementation of new model classes to the coding of some standard derivatives of the log-likelihood. Supplementary materials for this article are available online.

Gaussian · Model selection · Multivariate statistics · Parametric model · Parametric statistics · Quadratic equation · Scale parameter · Smoothing · Smoothing spline · Spline (mechanical) · Financial Risk and Volatility Modeling · Statistical Methods and Bayesian Inference · Statistical Methods and Inference