Hilbert space model for functional data

2012 ◽  
pp. 21-36
Author(s):  
Lajos Horváth ◽  
Piotr Kokoszka
Keyword(s):  
Hilbert Space ◽  
Functional Data ◽  
Space Model

On the existence of a Hilbert-space model for finite-valued observables

1992 ◽  
Vol 107 (12) ◽  
pp. 1413-1426 ◽  
Author(s):  
A. Fedullo
Keyword(s):  
Hilbert Space ◽  
Space Model

scholarly journals A functional Hodrick–Prescott filter

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Boualem Djehiche ◽  
Hiba Nassar
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Functional Data ◽  
Separable Hilbert Space ◽  
Underlying Distribution ◽  
Smoothing Operator ◽  
Infinite Dimensional ◽  
Optimal Smoothing ◽  
Functional Version

AbstractWe propose a functional version of the Hodrick–Prescott filter for functional data which take values in an infinite-dimensional separable Hilbert space. We further characterize the associated optimal smoothing operator when the associated linear operator is compact and the underlying distribution of the data is Gaussian.

scholarly journals A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space

2013 ◽  
Vol 7 (0) ◽  
pp. 2209-2240 ◽  
Author(s):  
Alessandra Menafoglio ◽  
Piercesare Secchi ◽  
Matilde Dalla Rosa
Keyword(s):  
Hilbert Space ◽  
Functional Data ◽  
Universal Kriging ◽  
Kriging Predictor

A proof of Hartman's theorem on compact Hankel operators

1975 ◽  
Vol 78 (3) ◽  
pp. 447-450 ◽  
Author(s):  
F. F. Bonsall ◽  
S. C. Power
Keyword(s):  
Hilbert Space ◽  
Compact Operator ◽  
Hankel Operator ◽  
Hankel Operators ◽  
Unilateral Shift ◽  
Space Model ◽  
Model Free ◽  
Multiplicity One ◽  
Image Position ◽  
Algebra Of Operators

Let U be a unilateral shift of arbitrary (perhaps uncountable) multiplicity on a Hilbert space. Following Rosenblum (5), an operator A is said to be a Hankel operator relative to U ifHartman (2) has characterized the compact Hankel operators relative to the unilateral shift of multiplicity one as the Hankel operators with symbol in H∞ + C(T). Using the usual function space model for representing the unilateral shift, Page ((4), theorem 10) has extended Hartman's theorem to unilateral shifts of countable multiplicity. We give a model-free proof of Hartman's theorem which applies to shifts of arbitrary multiplicity. The proof turns on the observation that a compact operator acts compactly on a certain algebra of operators.

scholarly journals Linear Processes for Functional Data

2018 ◽  
Author(s):  
André Mas ◽  
Besnik Pumo
Keyword(s):  
Hilbert Space ◽  
Functional Data ◽  
Statistical Models ◽  
Autoregressive Processes ◽  
Asymptotic Results ◽  
Linear Processes ◽  
Finite Dimensional ◽  
Convergence Results ◽  
General Estimation ◽  
General Method

This article provides an overview of the basic theory and applications of linear processes for functional data, with particular emphasis on results published from 2000 to 2008. It first considers centered processes with values in a Hilbert space of functions before proposing some statistical models that mimic or adapt the scalar or finite-dimensional approaches for time series. It then discusses general linear processes, focusing on the invertibility and convergence of the estimated moments and a general method for proving asymptotic results for linear processes. It also describes autoregressive processes as well as two issues related to the general estimation problem, namely: identifiability and the inverse problem. Finally, it examines convergence results for the autocorrelation operator and the predictor, extensions for the autoregressive Hilbertian (ARH) model, and some numerical aspects of prediction when the data are curves observed at discrete points.

$$\bar{p}N$$ Scattering with Annihilation Channel in an Extended Hilbert Space Model

1995 ◽  
pp. 409-414
Author(s):  
Yu. A. Kuperin ◽  
S. B. Levin ◽  
Yu. B. Melnikov ◽  
E. A. Yarevsky
Keyword(s):  
Hilbert Space ◽  
Annihilation Channel ◽  
Space Model

Derivation of a State-Space Model by Functional Data Analysis

2003 ◽  
Vol 18 (3-4) ◽  
pp. 533-546 ◽  
Author(s):  
Mariano J. Valderrama ◽  
Mónica Ortega-Moreno ◽  
Pedro González ◽  
Ana M. Aguilera
Keyword(s):  
Data Analysis ◽  
State Space ◽  
Functional Data Analysis ◽  
Functional Data ◽  
State Space Model ◽  
Space Model
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