Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields

1993 ◽  
Vol 45 (4) ◽  
pp. 503-512
Author(s):  
I. I. Deriev
Keyword(s):  
Asymptotic Normality ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Spherical Means ◽  
Nonlinear Functionals

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.

scholarly journals Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

2011 ◽  
Vol 2011 ◽  
pp. 1-35
Author(s):  
Sidi Ali Ould Abdi ◽  
Sophie Dabo-Niang ◽  
Aliou Diop ◽  
Ahmedoune Ould Abdi
Keyword(s):  
Asymptotic Normality ◽  
Random Fields ◽  
Quantile Function ◽  
Spatial Process ◽  
Kernel Estimate ◽  
Conditional Quantile ◽  
Conditional Quantile Estimator ◽  
Conditional Quantile Function ◽  
Mixing Sequence ◽  
Explicative Variable

Given a stationary multidimensional spatial process , we investigate a kernel estimate of the spatial conditional quantile function of the response variable given the explicative variable . Asymptotic normality of the kernel estimate is obtained when the sample considered is an -mixing sequence.

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

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