Theoretical properties of tests for spatial clustering of count data

Testing for spatial clustering of count data is an important problem in spatial data analysis. Several procedures have been proposed to this end but despite their extensive use, studies of their fundamental theoretical properties are almost non‐existent. The authors suggest two conditions that any reasonable test for spatial clustering should satisfy. The latter are based on the notion that the null hypothesis should be rejected almost surely as the amount of spatial clustering tends to infinity. The authors show that the chisquared test and the Potthoff—Whittinghill V have both properties but that other classical tests do not.     

Significance test of clustering under high dimensional setting with applications to cancer data

For high dimensional data, the SigClust is developed for testing the significance of clustering. The cluster index (CI) for SigClust is conducted by the ratio of the within-cluster and total sum of squares. But its empirical size is too conservative to be over controlled. By removing the cumbrous terms in the CI, an improved index (BCI) is proposed in this paper. The coefficient of variation of the BCI can be significantly reduced, implying that the new index BCI is stable. Moreover, the new significance test (NewSig) maintains the size, meanwhile, provides a greater power. Simulation experiments and two real cancer data examples are analysed for illustrating the performance of the new methodology.