2024/12/31 by Xavier Emery, Emery, Xavier, Moreno Bevilacqua +3 · 1 citation
Decision Sciences · Mathematics · #FOS: Computer and information sciences #Forecasting Techniques and Applications #Impact of AI and Big Data on Business and Society #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2501.00558
openalex publication_date 2024/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
A huge literature in statistics and machine learning is devoted to parametric families of correlation functions, where the correlation parameters are used to understand the properties of an associated spatial random process in terms of smoothness and global or compact support. However, most of current parametric correlation functions attain only non-negative values. This work provides two new families that parameterize negative dependencies (aka hole effects), along with smoothness, and global or compact support. They generalize the celebrated Matérn and Generalized Wendland models, respectively, which are attained as special cases. A link between the two new families is also established, showing that a specific reparameterization of the latter includes the former as a special limit case. Their performance in terms of estimation accuracy and goodness of best linear unbiased prediction is illustrated through synthetic and real data.