In this paper we survey some recent results on the central limit theorem and its weak
invariance principle for stationary sequences. We also describe several maximal …

A kernel method for realizing Bayes' rule is proposed, based on representations of
probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized …

This book offers a predominantly theoretical coverage of statistical prediction, with some
potential applications discussed, when data and/or parameters belong to a large or infinite …

Functional Gaussian Approximation for Dependent Structures develops and analyses
mathematical models for phenomena that evolve in time and influence each another. It …

We establish the asymptotic normality of the sample principal components of functional
stochastic processes under nonrestrictive assumptions which admit nonlinear functional …

A bootstrap procedure for functional time series is proposed which exploits a general vector
autoregressive representation of the time series of Fourier coefficients appearing in the …

The purpose of this paper is to derive sharp conditions for the asymptotic normality of a
discrete Fourier transform of a functional time series (X t: t≥ 1) defined, for all θ∈(− π, π], by …

In this paper, we give necessary and sufficient conditions for a stationary sequence of
random variables with values in a separable Hilbert space to satisfy the conditional central …

Abstract Let {X_k\} _ k ∈ Z ∈ L^ 2 (T) X kk∈ Z∈ L 2 (T) be a stationary process with
associated lag operators C _h C h. Uniform asymptotic expansions of the corresponding …

We consider autocovariance operators of a stationary stochastic process on a Polish space
that is embedded into a reproducing kernel Hilbert space. We investigate how empirical …