Global and local distance-based generalized linear models

Abstract

This paper introduces local distance-based generalized linear models. These models extend (weighted) distance-based linear models first to the generalized linear model framework. Then, a nonparametric version of these models is proposed by means of local fitting. Distances between individuals are the only predictor information needed to fit these models. Therefore, they are applicable, among others, to mixed (qualitative and quantitative) explanatory variables or when the regressor is of functional type. An implementation is provided by the R package dbstats, which also implements other distance-based prediction methods. Supplementary material for this article is available online, which reproduces all the results of this article.