Local Conformal Prediction For Non-Parametric Uncertainty Bands In Functional Ordinary Kriging

The prediction of spatial functional data, functions observed at spatial locations, represents a key aspect in many fields, including ecology, medicine and geosciences. A major challenge lies in providing reliable uncertainty quantification for predictions at unobserved sites. Traditional methods, such as Functional Ordinary Kriging (FOK) and Functional Universal Kriging (FUK), offer accurate spatial predictions; however, they often depend on strong assumptions and require computationally intensive resampling to construct prediction bands. Assessing uncertainty in Functional Ordinary Kriging (FOK) involves evaluating the variability in the predicted functions at unsampled locations. The process can include analyzing prediction variance, constructing confidence bands, using cross-validation, and applying simulation methods. Techniques such as resampling methods have been introduced to estimate the uncertainty in predicted curves, allowing for confidence bands for functional predictions. However, these are computationally intensive, especially for large datasets, due to the need for multiple resampling iterations. In addition, they may lead to biased estimates if the sample size is small or not representative of the population. In this work, we propose a Local Spatial Conformal Prediction (LSCP) method, which constructs prediction bands with finite-sample coverage guarantees without requiring strict distributional assumptions on residuals. LSCP adapts to spatial heterogeneity by selecting an adaptive neighborhood around each prediction site and modulates uncertainty along the functional domain using a spatial varibility measure. Unlike previous conformal approaches based on fixed spatial kernels, our method allows local adaptation in both space and function shape, enhancing flexibility and interpretability. Extensive simulations and a real-world application to the prediction of vegetation cycles in Fire Rings demonstrate that LSCP achieves accurate coverage and competitive band widths compared to existing kriging-based techniques. Our findings indicate that LSCP is a robust and computationally efficient alternative for uncer- tainty quantification in spatial functional data analysis.