On infinite dimensional periodically correlated random fields: Spectrum and evolutionary spectra

2016 ◽  
Vol 110 ◽  
pp. 257-267 ◽  
Author(s):  
H. Haghbin ◽  
Z. Shishebor
Keyword(s):  
Random Fields ◽  
Infinite Dimensional ◽  
Evolutionary Spectra

INFINITE DIMENSIONAL STATIONARY RANDOM FIELDS OVER A LOCALLY COMPACT ABELIAN GROUP

2012 ◽  
Vol 23 (04) ◽  
pp. 1250029
Author(s):  
HERBERT HEYER ◽  
M. M. RAO
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Locally Compact Abelian Group ◽  
Wide Sense ◽  
Euclidean Group ◽  
Locally Compact ◽  
Infinite Dimensional ◽  
Group Context ◽  
Stationary Random Fields ◽  
Lca Group

In this paper we consider spectral representation of infinite dimensional stationary random fields over an abelian locally compact (or LCA) group, and then extend the results of earlier authors who consider wide sense Markov random fields over a Euclidean group ℝn to the general LCA group context and obtain minimality properties. We also indicate possibilities of some extensions of these results to certain nonstationary classes.

scholarly journals SPHARMA approximations for stationary functional time series on the sphere

2021 ◽  
Author(s):  
Alessia Caponera
Keyword(s):  
Random Fields ◽  
Spectral Representation ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Stationary Processes ◽  
Representation Theorems ◽  
Infinite Dimensional ◽  
Functional Time Series ◽  
Moving Average Processes ◽  
Natural Way

AbstractIn this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressions (SPHAR) recently studied in Caponera and Marinucci (Ann Stat 49(1):346–369, 2021) and Caponera et al. (Stoch Process Appl 137:167–199, 2021); more importantly, we then show that SPHAR and SPHARMA processes of sufficiently large order can be exploited to approximate every isotropic and stationary sphere-cross-time random field, thus generalizing to this infinite-dimensional framework some classical results on real-valued stationary processes. Further characterizations in terms of functional spectral representation theorems and Wold-like decompositions are also established.

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

Sign in / Sign up

Export Citation Format

Share Document