City Research Online

Robust Fitting for Generalized Additive Models for Location, Scale and Shape

Aeberhard, W., Cantoni, E., Marra, G. and Radice, R. ORCID: 0000-0002-6316-3961 (2020). Robust Fitting for Generalized Additive Models for Location, Scale and Shape. Statistics and Computing,

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 assumption are known to mislead any likelihood-based inference and can hinder penalization schemes meant to ensure some degree of smoothness for non-linear effects. We propose a general approach to achieve robustness in fitting GAMLSSs by limiting the contribution of observations with low log-likelihood values. Robust selection of the smoothing parameters can be carried out either by minimizing information criteria that naturally arise from the robustified likelihood or via an extended Fellner-Schall method. The latter allows for automatic smoothing parameter selection and is particularly advantageous in applications with multiple smoothing parameters. We also address the challenge of tuning robust estimators for models with non-linear effects by proposing a novel median downweighting proportion criterion. This enables a fair comparison with existing robust estimators for the special case of generalized additive models, where our estimator competes favorably. The overall good performance of our proposal is illustrated by further simulations in the GAMLSS setting and by an application to functional magnetic resonance brain imaging using bivariate smoothing splines.

Publication Type: Article
Additional Information: This is a post-peer-review, pre-copyedit version of an article to be published in Statistics and Computing. The final authenticated version is to be available online at: http://link.springer.com/journal/11222
Publisher Keywords: Bounded influence function; Non-parametric regression; Penalized smoothing splines; Robust smoothing parameter selection; Robust information criterion
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HF Commerce > HF5601 Accounting
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: Business School > Actuarial Science & Insurance
Date Deposited: 20 Nov 2020 11:41
URI: https://openaccess.city.ac.uk/id/eprint/25296
[img] Text - Accepted Version
This document is not freely accessible due to copyright restrictions.

To request a copy, please use the button below.

Request a copy

Export

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login