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In this paper, I propose a general algorithm for multiple change pointanalysis via multivariate distribution-free nonparametric testing based on theconcept of ranks that are defined by measure transportation. Multivariate ranksand the usual one-dimensional ranks both share an important property: they areboth distribution-free. This finding allows for the creation of nonparametrictests that are distribution-free under the null hypothesis. This method hasapplications in a variety of fields, and in this paper I implement thisalgorithm to a microarray dataset for individuals with bladder tumors, an ECoGsnapshot for a patient with epilepsy, and in the context of trajectories ofCASI scores by education level and dementia status. Each change point denotes ashift in the rate of change of Cognitive Abilities score over years, indicatingthe existence of preclinical dementia. Here I will estimate the number ofchange points and each of their locations within a multivariate series oftime-ordered observations. This paper will examine the multiple change pointquestion in a broad setting in which the observed distributions and number ofchange points are unspecified, rather than assume the time series observationsfollow a parametric model or there is one change point, as many works in thisarea assume. The objective here is to create an algorithm for change pointdetection while making as few assumptions about the dataset as possible.Presented are the theoretical properties of this new algorithm and theconditions under which the approximate number of change points and theirlocations can be estimated. This algorithm has also been successfullyimplemented in the R package recp, which is available on GitHub. A section ofthis paper is dedicated to the execution of this procedure, as well as the useof the recp package.

Change Point Analysis of Multivariate Data: Using Multivariate  Rank-based Distribution-free Nonparametric Testing via Measure Transportation  with Applications in Tumor Microarrays and Dementia