We propose a novel family of test statistics to detect the presence of changepoints in a sequence of dependent, possibly multivariate, functional-valued observations. Our approach allows to test for a very general class of changepoints, including the "classical" case of changes in the mean, and even changes in the whole distribution. Our statistics are based on a generalisation of the empirical energy distance; we propose weighted functionals of the energy distance process, which are designed in order to enhance the ability to detect breaks occurring at sample endpoints. The limiting distribution of the maximally selected version of our statistics requires only the computation of the eigenvalues of the covariance function, thus being readily implementable in the most commonly employed packages, e.g. R. We show that, under the alternative, our statistics are able to detect changepoints occurring even very close to the beginning/end of the sample. In the presence of multiple changepoints, we propose a binary segmentation algorithm to estimate the number of breaks and the locations thereof. Simulations show that our procedures work very well in finite samples. We complement our theory with applications to financial and temperature data.

翻译：我们提出了一类新的检验统计量，用于检测依赖的、可能为多元的函数值观测序列中是否存在变点。该方法可检验非常广泛的变点类型，包括均值变化的"经典"情形，甚至能检测整个分布的变化。基于经验能量距离的推广，我们提出了能量距离过程的加权泛函，其设计旨在增强检测发生在样本端点附近的断点的能力。统计量最大选择版本的极限分布仅需计算协方差函数的特征值，因此可直接在常用软件包（如R）中实现。研究表明，在备择假设下，我们的统计量能够检测到发生在样本起始/结束点附近的变点。针对多个变点场景，我们提出了一种二元分割算法来估计断点数量及其位置。模拟实验显示，该方法在有限样本下表现优异。我们还通过金融数据与温度数据的应用对理论进行了补充验证。