scholarly journals Parametric Estimation of Long Memory Multivariate Gaussian random fields

2021 ◽  
Vol 16 (2) ◽  
pp. 2749-2766
Author(s):  
Aubin Yao N'dri ◽  
Amadou Kamagaté ◽  
Ouagnina Hili
Keyword(s):  
Random Fields ◽  
Long Memory ◽  
Almost Sure Convergence ◽  
Gaussian Random Fields ◽  
Parametric Estimation ◽  
Multivariate Gaussian ◽  
Finite Set ◽  
Multivariate Gaussian Random Fields ◽  
Distance Estimator ◽  
Set Of Points

The aim of this paper is to make a theoretically study of the minimum Hellinger distance estimator of multivariate, gaussian, stationary, isotropic long-memory random fields The variables are observed on a finite set of points in space. We establish under certain assumptions, the almost sure convergence and the asymptotic distribution of this estimator.

scholarly journals Parametric Estimation of Long Memory Multivariate Gaussian random fields

2021 ◽  
Vol 16 (2) ◽  
pp. 2747-2761
Author(s):  
Aubin Yao N'dri ◽  
Amadou Kamagaté ◽  
Ouagnina Hili
Keyword(s):  
Random Fields ◽  
Long Memory ◽  
Almost Sure Convergence ◽  
Gaussian Random Fields ◽  
Parametric Estimation ◽  
Multivariate Gaussian ◽  
Finite Set ◽  
Multivariate Gaussian Random Fields ◽  
Distance Estimator ◽  
Set Of Points

The aim of this paper is to make a theoretically study of the minimum Hellinger distance estimator of multivariate, gaussian, stationary, isotropic long-memory random fields The variables are observed on a finite set of points in space. We establish under certain assumptions, the almost sure convergence and the asymptotic distribution of this estimator.

Simulation of Multivariate Gaussian Fields Conditioned by Realizations of the Fields and Their Derivatives

1996 ◽  
Vol 63 (3) ◽  
pp. 758-765 ◽  
Author(s):  
Y. J. Ren ◽  
I. Elishakoff ◽  
M. Shinozuka
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Conditional Simulation ◽  
Gaussian Random Fields ◽  
Gaussian Field ◽  
Interpolation Technique ◽  
Multivariate Gaussian ◽  
Component Field ◽  
Multivariate Gaussian Random Fields ◽  
First Time

This paper investigates conditional simulation technique of multivariate Gaussian random fields by stochastic interpolation technique. For the first time in the literature a situation is studied when the random fields are conditioned not only by a set of realizations of the fields, but also by a set of realizations of their derivatives. The kriging estimate of multivariate Gaussian field is proposed, which takes into account both the random field as well as its derivative. Special conditions are imposed on the kriging estimate to determine the kriging weights. Basic formulation for simulation of conditioned multivariate random fields is established. As a particular case of uncorrelated components of multivariate field without realizations of the derivative of the random field, the present formulation includes that of univariate field given by Hoshiya. Examples of a univariate field and a three component field are elucidated and some numerical results are discussed. It is concluded that the information on the derivatives may significantly alter the results of the conditional simulation.

Covariance tapering for multivariate Gaussian random fields estimation

2015 ◽  
Vol 25 (1) ◽  
pp. 21-37 ◽  
Author(s):  
M. Bevilacqua ◽  
A. Fassò ◽  
C. Gaetan ◽  
E. Porcu ◽  
D. Velandia
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
Covariance Tapering ◽  
Multivariate Gaussian ◽  
Multivariate Gaussian Random Fields

scholarly journals The limiting spectral distribution in terms of spectral density

2016 ◽  
Vol 05 (01) ◽  
pp. 1650003 ◽  
Author(s):  
Costel Peligrad ◽  
Magda Peligrad
Keyword(s):  
Spectral Density ◽  
Rate Of Convergence ◽  
Large Class ◽  
Random Fields ◽  
Long Memory ◽  
Spectral Distribution ◽  
Complete Solution ◽  
Gaussian Random Fields ◽  
Stieltjes Transform ◽  
Counting Measure

For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists and we describe it via an equation satisfied by its Stieltjes transform. No rate of convergence to zero of correlations is imposed, therefore the process is allowed to have long memory. In particular, if the symmetrized matrices are constructed from stationary Gaussian random fields which have spectral density, the result of this paper gives a complete solution to the limiting eigenvalue distribution. More generally, for matrices whose entries are functions of independent and identically distributed random variables the result also holds.

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.

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