Cokriging for multivariate Hilbert space valued random fields: application to multi-fidelity computer code emulation

Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the underlying process fulfills some mixing conditions. As parametric inference in an infinite dimensional s...

Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition

In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced ρ-mixing condition.

Hilbert Space-valued Mixingales

Hilbert Space Valued Generalized Random Processes – Part I

Generalized random processes by various types of continuity are considered and classified as generalized random processes (GRPs) of type (I) and (II). Structure theorems for Hilbert space valued generalized random processes are obtained: Series expansion theorems for GRPs (I) considered as elements of the spaces L(A, S(H)−1) are derived, and structure representation theorems for GRPs (II) on K{...

Hilbert Space Valued Generalized Random Processes – Part Ii

Generalized random processes (GRPs) were classified as GRPs (I) and (II) in Part I of this paper. Now we focus our attention om GRPs (I), i.e. linear continuous mappings from a certain space of test functions to some space of classical or generalized random variables. The paper is organized in the following manner: In the introductory section (Section 1) we provide some basic terminology and no...