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Semiparametric estimation of spectral density function for irregular spatial data

Apr 18, 2014 - 9:00 AM
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Semiparametric estimation of spectral density function for irregular spatial data

 

Date: Friday, April 18
Time: 9:00 am -- 9:50 am
Place: Snedecor 1109
Speaker: Shu Yang, Department of Statistics, Iowa State University, Ames

Abstract:

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several nonparametric and semi-parametric methods has been developed to estimate the covariance structure based on the spectral representation of covariance functions. However, they either ignore the high frequency properties of the spectral density, which is essential to determine the performance of interpolation procedures such as kriging, or lack theoretical justifications. We propose a new semi-parametric method to estimate spectral densities of isotropic Gaussian processes with irregular observations. The spectral density function at low frequencies is estimated using smoothing spline, while a parametric model is used for the spectral density at high frequencies and the parameters estimated using method-of-moment based on empirical variogram at small lags. We derive the asymptotic bounds for bias and variance of the proposed estimator, and simulation results show that our method outperforms the existing nonparametric estimator by several performance criteria.

 Keywords: Irregular observations; Smoothing spline; Generalized cross validation; Decay rate; Integrated prediction error; Spatial interpolation;