# Nonparametric methods of assessing spatial isotropy

 Title: Nonparametric methods of assessing spatial isotropy Author: Guan, Yong Tao Abstract: A common requirement for spatial analysis is the modeling of the second -order structure . While the assumption of isotropy is often made for this structure , it is not always appropriate . A conventional practice to check for isotropy is to informally assess plots of direction -specific sample second -order properties , e .g . , sample variogram or sample second -order intensity function . While a useful diagnostic , these graphical techniques are difficult to assess and open to interpretation . Formal alternatives to graphical diagnostics are valuable , but have been applied to a limited class of models . In this dissertation , we propose a formal approach testing for isotropy that is both objective and appropriate for a wide class of models . This approach , which is based on the asymptotic joint normality of the sample second -order properties , can be used to compare these properties in multiple directions . An L _2 consistent subsampling estimator for the asymptotic covariance matrix of the sample second -order properties is derived and used to construct the test statistic with a limiting $\ \chi^2$ distribution under the null hypothesis . Our testing approach is purely nonparametric and can be applied to both quantitative spatial processes and spatial point processes . For quantitative processes , the results apply to both regularly spaced and irregularly spaced data when the point locations are generated by a homogeneous point process . In addition , the shape of the random field can be quite irregular . Examples and simulations demonstrate the efficacy of the approach . URI: http : / /hdl .handle .net /1969 .1 /1158 Date: 2004-11-15

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