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...

There has been a growing interest in using local statistics to identify spatial or spatiotemporal association patterns among georeferenced data, in which the null distributions of the statistics play a key role for the confirmatory inferences. In this study we focus on a generic form of local...

This article focuses on the estimation of the parametric component, which is of primary interest, in semi-varying coefficient models with heteroscedastic errors. Specifically, we first present a procedure for estimating the variance function of the error term and the resulting estimator is...

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>

Geographically weighted regression (GWR), as a useful method for exploring spatial nonstationarity of a regression relationship, has been applied to a variety of areas. In this method a spatially varying coefficient model is locally calibrated and the spatial-variation patterns of the locally...

Geographically weighted regression (GWR) is a way of exploring spatial nonstationarity by calibrating a multiple regression model which allows different relationships to exist at different points in space. Nevertheless, formal testing procedures for spatial nonstationarity have not been...

In recent years, there has been a growing interest in the use of local measures such as Anselin's LISAs and Ord and Getis <i>G </i>statistics to identify local patterns of spatial association. The statistical significance test based on local statistics is one of the most important aspects in performing...

A mixed geographically weighted regression (MGWR) model is a kind of regression model in which some coefficients of the explanatory variables are constant, but others vary spatially. It is a useful statistical modelling tool in a number of areas of spatial data analysis. After an MGWR model is...

Geographically weighted regression (GWR) is a useful technique for exploring spatial nonstationarity by calibrating, for example, a regression model which allows different relationships to exist at different points in space. In this line of research, many spatial data sets have been successfully...