Robust Fitting and Smoothing Parameter Selection for GAMLSS

• Activity Number: 81 - Regression, Distribution and Inference
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): William Aeberhard* and Eva Cantoni and Giampiero Marra and Rosalba Radice
• Companies: Stevens Institute of Technology and University of Geneva and University College London and City, University of London
• Keywords: Bounded influence function; Non-parametric regression; Penalized smoothing splines; Robust AIC

Abstract

The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such assumptions are known to throw off any likelihood-based inference and hinder penalization schemes meant to ensure some degree of smoothness for non-linear effects approximated by linear combinations of basis functions. We propose a general approach to achieve robustness in fitting GAMLSSs by limiting the contribution of observations whose log-likelihood value is too low. Parameter estimates are thus resistant to potentially outlying observations. Robust selection of the smoothing parameters is carried out thanks to an approximate robust Akaike Information Criterion that can be directly derived from the robustified likelihood. Moreover, we address the difficult task of tuning robust estimators when fitting non-linear additive effects by proposing a novel median downweighting proportion criterion. The good performance of the robust estimator is illustrated by simulations and by an application to brain imaging with bivariate smoothing splines.