  In this article, we propose a class of test statistics for a change point in
the mean of high-dimensional independent data. Our test integrates the
U-statistic based approach in a recent work by \cite{hdcp} and the $L_q$-norm
based high-dimensional test in \cite{he2018}, and inherits several appealing
features such as being tuning parameter free and asymptotic independence for
test statistics corresponding to even $q$s. A simple combination of test
statistics corresponding to several different $q$s leads to a test with
adaptive power property, that is, it can be powerful against both sparse and
dense alternatives. On the estimation front, we obtain the convergence rate of
the maximizer of our test statistic standardized by sample size when there is
one change-point in mean and $q=2$, and propose to combine our tests with a
wild binary segmentation (WBS) algorithm to estimate the change-point number
and locations when there are multiple change-points. Numerical comparisons
using both simulated and real data demonstrate the advantage of our adaptive
test and its corresponding estimation method.
