Bootstrap based uncertainty bands for prediction in functional kriging

TL;DR

This paper introduces a semi-parametric bootstrap method to accurately quantify uncertainty in spatially correlated functional data predictions, maintaining spatial dependence in the bootstrap samples.

Contribution

It presents a novel bootstrap approach for uncertainty estimation in functional kriging with external drift, addressing a key open issue in spatial functional data analysis.

Findings

Method effectively quantifies uncertainty in predictions.

Approach maintains spatial dependence in bootstrap samples.

Validated through simulations and real data applications.

Abstract

The increasing interest in spatially correlated functional data has led to the development of appropriate geostatistical techniques that allow to predict a curve at an unmonitored location using a functional kriging with external drift model that takes into account the effect of exogenous variables (either scalar or functional). Nevertheless uncertainty evaluation for functional spatial prediction remains an open issue. We propose a semi-parametric bootstrap for spatially correlated functional data that allows to evaluate the uncertainty of a predicted curve, ensuring that the spatial dependence structure is maintained in the bootstrap samples. The performance of the proposed methodology is assessed via a simulation study. Moreover, the approach is illustrated on a well known data set of Canadian temperature and on a real data set of PM$_{10}$ concentration in the Piemonte region, Italy. Based on the results it can be concluded that the method is computationally feasible and suitable for quantifying the uncertainty around a predicted curve. Supplementary material including R code is available upon request.