Spatial Association of Qualitative Data: A New Test Using Symbolic Dynamics

In the present paper, we construct a simple, consistent and powerful test for qualitative spatial independence, called the TG test, by using symbolic dynamics and symbolic entropy as a measure of spatial dependence. We also give a standard asymptotic distribution of an affine transformation of the symbolic entropy under the null hypothesis of independence in the spatial qualitative process. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We include numerical experiments to demonstrate the finite sample behaviour of the test, and an empirical application of spatial association of fast food establishments in the city of Toronto, Canada.