Abstract

Local dependence is common in multivariate and object data sequences. We consider the testing and estimation of change-points in such sequences. A new way of permutation, circular block permutation with a random starting point, is proposed and studied for a scan statistic utilizing graphs representing the similarity between observations. The proposed permutation approach could correctly address for local dependence and make it possible the theoretical treatments for the non-parametric graph-based scan statistic for locally dependent data. We derive accurate analytic approximations to the significance of graph-based scan statistics under the circular block permutation framework, facilitating its application to locally dependent multivariate or object data sequences.