  In this paper, I propose a general algorithm for multiple change point
analysis via multivariate distribution-free nonparametric testing based on the
concept of ranks that are defined by measure transportation. Multivariate ranks
and the usual one-dimensional ranks both share an important property: they are
both distribution-free. This finding allows for the creation of nonparametric
tests that are distribution-free under the null hypothesis. This method has
applications in a variety of fields, and in this paper I implement this
algorithm to a microarray dataset for individuals with bladder tumors, an ECoG
snapshot for a patient with epilepsy, and in the context of trajectories of
CASI scores by education level and dementia status. Each change point denotes a
shift in the rate of change of Cognitive Abilities score over years, indicating
the existence of preclinical dementia. Here I will estimate the number of
change points and each of their locations within a multivariate series of
time-ordered observations. This paper will examine the multiple change point
question in a broad setting in which the observed distributions and number of
change points are unspecified, rather than assume the time series observations
follow a parametric model or there is one change point, as many works in this
area assume. The objective here is to create an algorithm for change point
detection while making as few assumptions about the dataset as possible.
Presented are the theoretical properties of this new algorithm and the
conditions under which the approximate number of change points and their
locations can be estimated. This algorithm has also been successfully
implemented in the R package recp, which is available on GitHub. A section of
this paper is dedicated to the execution of this procedure, as well as the use
of the recp package.
