A p - 1 random vector x is said to have a spherical distribution, if for every p - p orthogonal matrix Q, x and Qx have the same distribution. In this paper, some nonparametric goodness of fit Wilcoxon-type tests for sphericity are proposed. Some results on the limiting distributions of the...

Recently, Ord and Getis (Ann Reg Sci 48:529–539, <CitationRef CitationID="CR15">2012</CitationRef>) developed a local statistic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$H_i$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>H</mi> <mi>i</mi> </msub> </math> </EquationSource> </InlineEquation>, called local spatial heteroscedasticity statistic, to identify boundaries of clusters and to describe the nature of heteroscedasticity within clusters. Furthermore, in order to implement the...</equationsource></equationsource></inlineequation></citationref>