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 …
P Kokoszka, M Reimherr - Stochastic Processes and their Applications, 2013 - Elsevier
We establish the asymptotic normality of the sample principal components of functional stochastic processes under nonrestrictive assumptions which admit nonlinear functional …
E Paparoditis - The annals of Statistics, 2018 - JSTOR
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 …
C Cerovecki, S Hörmann - Journal of multivariate analysis, 2017 - Elsevier
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 …
J Dedecker, F Merlevède - Stochastic processes and their applications, 2003 - Elsevier
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 …
M Jirak - Probability Theory and Related Fields, 2016 - Springer
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 …