Nonparametric Methods for Estimating Nonstationary Covariance Functions on Spheres

• Activity Number: 601
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Zhengyuan Zhu*+ and Yang Li
• Companies: Iowa State University and Iowa State University
• Keywords: spatial statistics ; krigging ; Legendre polynomials ; axially symmeric ; Matern

Abstract

Spatial analyses of large data sets on spheres have drawn more attention recently. In this talk we consider the problem of estimating the non-stationary covariance structure of random processes on spheres. Conventional full likelihood approaches require full specification of parametric models. They also face the computational obstacle of computing the inverse and determinant of covariance matrix. Alternatively, nonparametric methods which do no require subjective specification of a parametric form of the covariance structure can be utilized. We will describe methods based on constrained expansion of Legendre polynomials and kernel convolution which are flexible enough to describe the spatial variation at both global and local scales, and develop efficient algorithms for model estimation. Simulation results and an application to a global ozone data set will be presented to illustrate the advantage of the proposed methods.