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Title: A general frequency domain method for assessing spatial covariance structures Authors:  Soumendra Lahiri - North Carolina State University (United States)
Daniel Nordman - Iowa State University (United States)
Soutir Bandyopadhyay - Colorado School of Mines (United States) [presenting]
Abstract: In examining dependence in spatial data, it can be helpful to assess hypotheses about spatial covariance that may not be fully model-based or parametric. That is, one may wish to test for general features regarding spatial covariance without presupposing any particular, or potentially restrictive, assumptions about the joint data distribution. Current methods for testing spatial covariance are often intended for specialized inference scenarios, usually with spatial lattice data. We propose instead a general method for estimation and testing of spatial covariance structure, which is valid for a variety of inference problems (including nonparametric hypotheses) and applies to a large class of spatial sampling designs with irregular data locations. The proposed method has the advantage of providing valid inference in the frequency domain without estimation of such standard errors, which are often intractable, and without particular distributional assumptions about the data (e.g., Gaussianity). To illustrate that, we develop the method for formally testing isotropy and separability in spatial covariance and consider confidence regions for spatial parameters in variogram model fitting. A broad result is also presented to validate the method for further general tests of spatial covariance structure. The approach uses spatial test statistics, based on an extended version of empirical likelihood, having simple chi-square limits for calibrating tests.