• Corpus ID: 53654185

Covariance tapering for anisotropic nonsta-tionary Gaussian random fields with appli-cation to large scale spatial data sets

@inproceedings{Safikhani2014CovarianceTF,
  title={Covariance tapering for anisotropic nonsta-tionary Gaussian random fields with appli-cation to large scale spatial data sets},
  author={Abolfazl Safikhani and Yimin Xiao},
  year={2014}
}
Estimating the covariance structure of spatial random processes is an important step in spatial data analysis. Maximum likelihood estimation is a popular method in spatial models based on Gaussian random fields. But calculating the likelihood in large scale data sets is computationally infeasible due to the heavy computation of the precision matrix. One way to mitigate this issue, which is due to Furrer et al. (2006), is to “taper” the covariance matrix. While most of the results in the current… 

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References

SHOWING 1-10 OF 12 REFERENCES

Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets

TLDR
Focusing on the particular case of the Matérn class of covariance functions, this article gives conditions under which estimators maximizing the tapering approximations are, like the maximum likelihood estimator, strongly consistent.

Local likelihood estimation for nonstationary random fields

Fixed-domain asymptotic properties of tapered maximum likelihood estimators

When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is

Fixed rank kriging for very large spatial data sets

Summary.  Spatial statistics for very large spatial data sets is challenging. The size of the data set, n, causes problems in computing optimal spatial predictors such as kriging, since its

Covariance Tapering for Interpolation of Large Spatial Datasets

TLDR
It is shown that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and still leads to an asymptotically optimal mean squared error.

Some theory for anisotropic processes on the sphere

Fractal and smoothness properties of space-time Gaussian models

Spatio-temporal models are widely used for inference in statistics and many applied areas. In such contexts, interests are often in the fractal nature of the sample surfaces and in the rate of change

Some Classes of Random Fields in n-Dimensional Space, Related to Stationary Random Processes

TLDR
A spectral theory for certain types of random fields and random generalized fields (multidimensional random distributions) in the Euclidean n-space $R_n $ similar to the well-known spectral theories for stationary random processes is established.

On Absolute Continuity of Measures Corresponding to Homogeneous Gaussian Fields

General questions of absolute continuity and singularity of Gaussian measures have been considered in works of Ya. Gaek [1], J. Feldman [2] and Yu. A. Rozanov 3]. However, in considering concrete

Interpolation of Spatial Data: Some Theory for Kriging

TLDR
This chapter discusses the role of asymptotics for BLPs, and applications of equivalence and orthogonality of Gaussian measures to linear prediction, and the importance of Observations not part of a sequence.