Testing local versions of correlation coefficients

The aim of this paper is to define and test local versions of standard correlation coefficients in statistical analysis. This research is motivated by the increasing number of applications using local versions of explanatory spatial data analysis methods such as local regression. Local statistical methods should be applied together with local measures of statistical inference in order to check their performance and to provide an indication of the quality of their results. One example of local explanatory data analysis method is the Geographically Weighted Regression, the application of which allows the researcher to check for the existence of spatial nonstationarity in the relationships between a geographic phenomenon and its determinants. In this paper, a local version of Pearson correlation coefficient is defined and applied to internal migration data in Sweden. The results suggest that globally independent variables are not necessarily independent locally, thus the independence criterion may be violated when local regression analysis is performed. Thus, the results of local regression analysis should be presented in light of the local statistical inference and their interpretation should be made with care. Copyright Springer-Verlag 2012