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.

翻译：序贯变化检测是一个经典问题，具有广泛的应用。然而，先前的大部分工作都基于参数方法，例如聚焦于指数族分布。本文针对变化前和变化后分布均为非参数指定（因此为复合分布）的情形，提出了一种全新且通用的序贯变化检测框架。我们的过程具有清晰且非渐近的平均运行长度（虚警频率）界限。在特定的非参数情形（如次高斯或次指数分布）下，我们还提供了变化点后检测延迟的近乎最优界限。我们引入的核心技术工具称为“e-检测器”，它由逐次启动的e-过程（非负上鞅的基本推广）的和构成。我们首先介绍了简单的Shiryaev-Roberts和CUSUM型e-检测器，随后展示了如何设计其混合形式以实现统计效率和计算效率的双重优化。我们的e-检测器框架可实例化以恢复参数问题中经典的基于似然的方法，同时为许多非参数问题提供了首个变化检测方法。作为贯穿全文的实例，我们解决了在无独立同分布假设下检测有界随机变量均值变化的问题，并将其应用于跟踪一支篮球队跨多个赛季的表现。