Estimation of Non-stationary Covariance Function with/without Replications

Oregon Convention Center 

Spatial statistics frequently involve modeling (transformed) data by a Gaussian process F, but the covariance of F may NOT be stationary. In the context of replicated observations of a Gaussian spatial field, this study introduces a nonparametric approach applicable for a general covariance function that may be non-stationary. For situations where only a single observation is available with no replication, a local block bootstrap procedure is proposed to generate additional observations. We compare the estimated covariance obtained through the empirical method with those from parametric and nonparametric methodologies. We discuss the strengths and limitations of each approach in capturing the complex covariance structure inherent in spatial data.

Gaussian process

non-stationary

nonparametric

bootstrap

Covariance Function 

Section on Nonparametric Statistics