A Hilbert space is an infinite dimensional functional space. That is to say, it is a vector space composed of an infinite set of orthogonal functions. The orthogonality of a Hilbert space is defined by the integral over the appropriate interval of the...

The mathematical concept of a Hilbert space, named after the German mathematician David Hilbert, generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the two-dimensional plane and three-dimensional space to...

This book shows how probability and statistical inference can be defined in terms of a Hilbert space by replacing the classical definition using sample space with an equivalent Hilbert space. The major motivation for this replacement approach is to enhance the interpretation of...

ABSTRACT Reproducing kernel Hilbert spaces regression procedures for prediction of total genetic value for quantitative traits, which make use of phenotypic and genomic data simultaneously, are discussed from a theoretical perspective. It is argued that a nonparametric treatment may be needed for capturing...