On the spectral density and asymptotic normality of weakly dependent random fields

1992 ◽  
Vol 5 (2) ◽  
pp. 355-373 ◽  
Author(s):  
Richard C. Bradley
Keyword(s):  
Spectral Density ◽  
Asymptotic Normality ◽  
Random Fields ◽  
Weakly Dependent

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 Generalised spectral analysis of fractional random fields

1997 ◽  
Vol 62 (1) ◽  
pp. 64-83
Author(s):  
V. V. Anh ◽  
K. E. Lunney
Keyword(s):  
Spectral Analysis ◽  
Spectral Density ◽  
Long Range ◽  
Random Fields ◽  
Spectral Decomposition ◽  
Covariance Function ◽  
Long Range Dependence ◽  
Type Condition ◽  
Fractal Index ◽  
Fractal Characteristics

AbstractThis paper considers a large class of non-stationary random fields which have fractal characteristics and may exhibit long-range dependence. Its motivation comes from a Lipschitz-Holder-type condition in the spectral domain.The paper develops a spectral theory for the random fields, including a spectral decomposition, a covariance representation and a fractal index. From the covariance representation, the covariance function and spectral density of these fields are defined. These concepts are useful in multiscaling analysis of random fields with long-range dependence.

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