  Sequential change detection is a classical problem with a variety of
applications. However, the majority of prior work has been parametric, for
example, focusing on exponential families. We develop a fundamentally new and
general framework for sequential change detection when the pre- and post-change
distributions are nonparametrically specified (and thus composite). Our
procedures come with clean, nonasymptotic bounds on the average run length
(frequency of false alarms). In certain nonparametric cases (like sub-Gaussian
or sub-exponential), we also provide near-optimal bounds on the detection delay
following a changepoint. The primary technical tool that we introduce is called
an \emph{e-detector}, which is composed of sums of e-processes -- a fundamental
generalization of nonnegative supermartingales -- that are started at
consecutive times. We first introduce simple Shiryaev-Roberts and CUSUM-style
e-detectors, and then show how to design their mixtures in order to achieve
both statistical and computational efficiency. Our e-detector framework can be
instantiated to recover classical likelihood-based procedures for parametric
problems, as well as yielding the first change detection method for many
nonparametric problems. As a running example, we tackle the problem of
detecting changes in the mean of a bounded random variable without i.i.d.
assumptions, with an application to tracking the performance of a basketball
team over multiple seasons.
