  We investigate sequential change point estimation and detection in univariate
nonparametric settings, where a stream of independent observations from
sub-Gaussian distributions with a common variance factor and piecewise-constant
but otherwise unknown means are collected. We develop a simple CUSUM-based
methodology that provably control the probability of false alarms or the
average run length while minimizing, in a minimax sense, the detection delay.
We allow for all the model parameters to vary in order to capture a broad range
of levels of statistical hardness for the problem at hand. We further show how
our methodology is applicable to the case in which multiple change points are
to be estimated sequentially.
