2021/06/26 by V. A. Menegatto, V. A. Menegatto, Menegatto, V. A. +2
Environmental Science · Mathematics · #42A8 - 47A56 #Advanced Statistical Methods and Models #Applied mathematics #Artificial intelligence #Bounded function #Cartesian product #Computer science #Discrete mathematics #FOS: Mathematics #Functional Analysis (math.FA) #Generalization #Interpolation (computer graphics) #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Monotone polygon #Multivariate statistics #Parametric statistics #Positive-definite matrix #Product (mathematics) #Pure mathematics #Soil Geostatistics and Mapping #Statistical and numerical algorithms #Statistics #math.FA #msc:42A8 #msc:47A56
paper · pdf · doi:10.48550/arxiv.2106.14064
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/06/26 · openalex publication_date 2021/06/26 · arxiv updated 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We introduce a method to construct general multivariate positive definite kernels on a nonempty set X that employs a prescribed bounded completely monotone function and special multivariate functions on X. The method is consistent with a generalized version of Aitken's integral formula for Gaussians. In the case where X is a cartesian product, the method produces nonseparable positive definite kernels that may be useful in multivariate interpolation. In addition, it can be interpreted as an abstract multivariate generalization of the well-established Gneiting's model for constructing space-time covariances commonly cited in the literature. Many parametric models discussed in statistics can be interpreted as particular cases of the method.