Matrix valued positive definite kernels related to the generalized Aitken's integral for Gaussians

2021/06/26 by V‎. ‎A‎. Menegatto, Menegatto, V. A., C. P. Oliveira +1
Environmental Science · Mathematics · #42A8 - 47A56 #Advanced Statistical Methods and Models #FOS: Mathematics #Functional Analysis (math.FA) #Soil Geostatistics and Mapping #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2106.14064

openalex publication_date 2021/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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