Composite Likelihood Inference for Multivariate Gaussian Random Fields

2016 ◽  
Vol 21 (3) ◽  
pp. 448-469 ◽  
Author(s):  
Moreno Bevilacqua ◽  
Alfredo Alegria ◽  
Daira Velandia ◽  
Emilio Porcu
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
Composite Likelihood ◽  
Likelihood Inference ◽  
Multivariate Gaussian ◽  
Multivariate Gaussian Random Fields

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.

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.

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.

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 Geostatistics of extremes

2011 ◽  
Vol 468 (2138) ◽  
pp. 581-608 ◽  
Author(s):  
A. C. Davison ◽  
M. M. Gholamrezaee
Keyword(s):  
Spatial Domain ◽  
Gaussian Random Fields ◽  
Information Criteria ◽  
Composite Likelihood ◽  
Model Fit ◽  
Likelihood Inference ◽  
Stable Model ◽  
Competing Models ◽  
Maximum Temperatures ◽  
Occurrence Times

We describe a prototype approach to flexible modelling for maxima observed at sites in a spatial domain, based on fitting of max-stable processes derived from underlying Gaussian random fields. The models we propose have generalized extreme-value marginal distributions throughout the spatial domain, consistent with statistical theory for maxima in simpler cases, and can incorporate both geostatistical correlation functions and random set components. Parameter estimation and fitting are performed through composite likelihood inference applied to observations from pairs of sites, with occurrence times of maxima taken into account if desired, and competing models are compared using appropriate information criteria. Diagnostics for lack of model fit are based on maxima from groups of sites. The approach is illustrated using annual maximum temperatures in Switzerland, with risk analysis proposed using simulations from the fitted max-stable model. Drawbacks and possible developments of the approach are discussed.

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