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：序列变化检测是一个经典问题，应用广泛。然而，以往的研究大多基于参数化方法，例如聚焦于指数族分布。我们开发了一种全新且通用的框架，用于当变化前和变化后分布为非参数化指定（因此为复合分布）时的序列变化检测。我们的方法在平均运行长度（误报频率）方面具有清晰、非渐近的界。在某些非参数化情形下（如次高斯或次指数分布），我们还提供了变化点后检测延迟的近最优界。我们引入的主要技术工具称为“e-detector”，它由从连续时间点开始的e-过程之和构成——e-过程是非负超鞅的基本推广。我们首先介绍简单的Shiryaev-Roberts型与CUSUM型e-detector，然后展示如何设计其混合版本以实现统计与计算效率兼得。我们的e-detector框架可实例化以恢复参数化问题中的经典基于似然的方法，同时为许多非参数化问题提供了首个变化检测方法。作为贯穿性示例，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，并应用于跟踪一支篮球队多个赛季的表现。