  Change-point detection has been a classical problem in statistics and
econometrics. This work focuses on the problem of detecting abrupt
distributional changes in the data-generating distribution of a sequence of
high-dimensional observations, beyond the first two moments. This has remained
a substantially less explored problem in the existing literature, especially in
the high-dimensional context, compared to detecting changes in the mean or the
covariance structure. We develop a nonparametric methodology to (i) detect an
unknown number of change-points in an independent sequence of high-dimensional
observations and (ii) test for the significance of the estimated change-point
locations. Our approach essentially rests upon nonparametric tests for the
homogeneity of two high-dimensional distributions. We construct a single
change-point location estimator via defining a cumulative sum process in an
embedded Hilbert space. As the key theoretical innovation, we rigorously derive
its limiting distribution under the high dimension medium sample size (HDMSS)
framework. Subsequently we combine our statistic with the idea of wild binary
segmentation to recursively estimate and test for multiple change-point
locations. The superior performance of our methodology compared to other
existing procedures is illustrated via extensive simulation studies as well as
over stock prices data observed during the period of the Great Recession in the
United States.
