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

Authors : Valdir MENEGATTO, Claudemir OLİVEİRA

Pages : 384-399

Doi:10.33205/cma.964096

View : 13 | Download : 5

Publication Date : 2021-12-13

Article Type : Research Paper

Abstract :We introduce a method to construct general multivariate positive definite kernels on a nonempty set X X that employs a prescribed bounded completely monotone function and special multivariate functions on X X . The method is consistent with a generalized version of Aitken`s integral formula for Gaussians. In the case in which X 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 version of the well-established Gneiting`s model for constructing space-time covariances commonly highly cited in the literature. Many parametric models discussed in statistics can be interpreted as particular cases of the method.
Keywords : positive definite kernels, conditionally negative definite functions, Aitken`s integral, Schur exponential, Oppenheim`s inequality, Gneiting`s model