According to Anselin, a LISA statistic have to satisfy two requirements:
- The LISA for each observation gives an indicator of the extent of significant spatial clustering of similar values around that observation.
- The sum of LISAs for all observations is proportional to a global indicator of spatial association.
The second requirement is very straightforward but I cannot understand mathematically the first requirement.
For example, he said in his paper:
The L_i should be such that it is possible to infer the statistical significance of the patter of spatial association at location i. More formally, this requires the operationalization of a statement such as Prob[L_i>δ_i]≤α_i...
Is this the first requirement?