  In this paper, I propose a general procedure for multivariate
distribution-free nonparametric testing derived from the concept of ranks that
are based upon measure transportation in the context of multiple change point
analysis. I will use this algorithm to estimate both the number of change
points and their locations within an observed multivariate time series. In this
paper, the change point problem is observed in a general setting in which both
the given distribution and number of change points are unknown, rather than
assume the observed time series follows a specific distribution or contains
only one change point as many works in this area of study assume. The intention
of this is to develop a technique for accurately identifying the changes in a
distribution while making as few suppositions as possible. The rank energy
statistic used here is based on energy statistics and has the potential to
detect any change in a distribution. I present the properties of this new
algorithm, which can be used to analyze various datasets, including
hierarchical clustering, testing multivariate normality, gene selection, and
microarray data analysis. This algorithm has also been implemented in the R
package recp, which is available on GitHub.
