Distribution free prediction for geographically weighted functional regression models

Abstract

Recently, there has been significant interest in distribution-free prediction within the fields of machine learning and statistics. Distribution-free prediction involves techniques that aim to make predictions or create prediction intervals without relying on explicit assumptions about the underlying distribution of the data. In this study, we introduce an inductive conformal prediction strategy specifically designed for spatio-functional data. We define a prediction with a conformity level for the response of two distinct regression models: a Geographically Weighted Functional Regression model and its heteroscedastic version. We propose two novel measures of non-conformity and prediction bands for the functional response variable. The properties of the resulting estimates are examined through simulation and real data analysis on air quality data.