2020/06/28 by Huiying Mao, Mao, Huiying, Ryan Martin +3 · 2 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2006.15640
openalex publication_date 2020/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of misspecification bias that can negatively affect their validity. Here we present a new approach for model-free nonparametric spatial prediction based on the conformal prediction machinery. Our key observation is that spatial data can be treated as exactly or approximately exchangeable in a wide range of settings. In particular, under an infill asymptotic regime, we prove that the response values are, in a certain sense, locally approximately exchangeable for a broad class of spatial processes, and we develop a local spatial conformal prediction algorithm that yields valid prediction intervals without strong model assumptions like stationarity. Numerical examples with both real and simulated data confirm that the proposed conformal prediction intervals are valid and generally more efficient than existing model-based procedures for large datasets across a range of non-stationary and non-Gaussian settings.