A note on the SG(m) Test

ABSTRACT López et al. (Reg Sci Urban Econ 40(2–3):106–115, 2010) introduce a nonparametric test of spatial dependence, called SG(m). The test is claimed to be consistent and asymptotically Chi-square distributed. Elsinger (Reg Sci Urban Econ 43(5):838–840, 2013) raises doubts about the two properties. Using a particular counterexample, he shows that the asymptotic distribution of the SG(m) test may be far from the Chi-square family; the property of consistency is also questioned. In this note, the authors want to clarify the properties of the SG(m) test. We argue that the cause of the conflict is in the specification of the symbolization map. The discrepancies can be solved by adjusting some of the definitions made in the original paper. Moreover, we introduce a permutational bootstrapped version of the SG(m) test, which is powerful and robust to the underlying statistical assumptions. This bootstrapped version may be very useful in an applied context