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A frequency domain empirical likelihood for estimation and testing of spatial covariance structure

May 16, 2015 - 9:00 AM
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A frequency domain empirical likelihood for estimation and testing of spatial covariance structure

 

Date: Friday, May 16
Time: 9:00 am -- 9:50 am
Place: Snedecor 2102
Speaker: Matthew Van Hala, Department of Statistics, Iowa State University, Ames

Abstract:

This talk considers a general empirical likelihood (EL) method for spatial data with irregularly spaced locations, which is formulated in the frequency domain for estimation and testing of spatial covariance structures. A general nonparametric method is proposed for inference about spatial covariance structures based on a frequency domain empirical likelihood (FDEL), which is shown to be valid for a large class of spatial sampling designs, allowing irregularly spaced data locations and varying levels of infill sampling. In comparison to (regularly spaced) time series and spatial lattice data, the spectral analysis of irregularly located spatial data presents significant challenges. One serious complication is that spatial statistics under this general data generation framework have limiting distributions that depend intricately on a number of factors, including the underlying spatial asymptotic framework (i.e., rate of infill sampling), the unknown distribution of sampling locations, and the exact process distributional structure. The proposed spatial FDEL method has the advantage of providing valid inference without knowledge, assumptions or explicit estimation of these factors. The method's formulation relies upon general spectral estimating equations for use in a broad range of spatial testing and estimation problems. Log-likelihood ratio statistics, based on the maximum EL estimation in the spectral domain, have chi-square limits regardless of the asymptotic framework, and these EL statistics can be applied to calibrate tests of spatial covariance structures as well as nonparametric confidence regions for spatial parameters.