$K$-Differenced Vector Random Fields

Abstract

supported me and given me strength to come to this point. This dissertation would not have been possible without the guidance and help of several individuals who, in one way or another, have contributed and extended their valuable assistance in the preparation and completion of this study. My first debt of gratitude goes to my advisor, Professor Chunseng Ma, who has truly been an inspiration. Without his invaluable guidance, this dissertation would not have been possible. I would also like to express my gratitude to all the members of my committee for the contribution of their valuable time.

Covariance Models for Multivariate Random Fields resulting from Pseudo Cross-Variograms

“…Additive separable conditionally negative definite kernels are also used in Corollary 2 in Alsultan and Ma (2019). The latter is based on Theorem 2 in Alsultan and Ma (2019), which can be concretized via Theorem 2.1.…”

“…Additive separable conditionally negative definite kernels are also used in Corollary 2 in Alsultan and Ma (2019). The latter is based on Theorem 2 in Alsultan and Ma (2019), which can be concretized via Theorem 2.1. In fact, the matrix-valued kernels g = (g ij ) i,j=1,...,m given there are exactly the positive conditionally negative definite matrixvalued kernels as introduced in Section 2.…”