Bootstrap tests for the equality of distributions

Testing equality of two and k distributions has long been an interesting issue in statistical inference. To overcome the sparseness of data points in high-dimensional space and deal with the general cases, we suggest several projection pursuit type statistics. Some results on the limiting distributions of the statistics are obtained. Some properties of Bootstrap approximation are investigated. Furthermore, for computational reasons an approximation for the statistics the based on Number theoretic method is applied. Several simulation experiments are performed.