Estimation of Spatial Deformation for Nonstationary Processes via Variogram Alignment

Spectral methods for nonstationary spatial processes

We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the proposed estimators via shrinking asymptotics, assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound. With this type of asymptotic ...

Nonparametric Estimation of Spatial Risk for a Mean Nonstationary Random Field}

The common methods for spatial risk estimation are investigated for a stationary random field. Because of simplifying, lets distribution is known, and parametric variogram for the random field are considered. In this paper, we study a nonparametric spatial method for spatial risk. In this method, we model the random field trend by a local linear estimator, and through bias-corrected residuals, ...

Variogram Model Selection via Nonparametric Derivative Estimation

Before optimal linear prediction can be performed on spatial data sets, the variogram is usually estimated at various lags and a parametric model is fitted to those estimates. Apart from possible a priori knowledge about the process and the user’s subjectivity, there is no standard methodology for choosing among valid variogram models like the spherical or the exponential ones. This paper discu...

Modeling and Prediction of Nonstationary Spatial Processes

Bayesian Inference for Nonstationary Spatial Covariance Structure via Spatial Deformations

In geostatistics it is common practice to assume that the underlying spatial process is stationary and isotropic, that is the spatial distribution is unchanged when the origin of the index set is translated and the process is stationary under rotations about the origin. However in environmental problems, it is not very realistic to make such assumptions since local innuences in the correlation ...