Valid Model-Free Spatial Prediction

• 成果类型: Article
• 署名作者: Mao, Huiying; Martin, Ryan; Reich, Brian J. J.
• 署名单位: North Carolina State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2147531
• 发表日期: 2024
• 页码: 904-914
• 关键词: framework

摘要

Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in nonstationary 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 nonstationary and non-Gaussian settings.