In this article we describe a new Hermite series based sequential estimator for the Spearman rank correlation coefficient and provide algorithms applicable in both the stationary and non-stationary settings. To treat the non-stationary setting, we introduce a novel, exponentially weighted estimator for the Spearman rank correlation, which allows the local nonparametric correlation of a bivariate data stream to be tracked. To the best of our knowledge this is the first algorithm to be proposed for estimating a time varying Spearman rank correlation that does not rely on a moving window approach. We explore the practical effectiveness of the Hermite series based estimators through real data and simulation studies demonstrating good practical performance. The simulation studies in particular reveal competitive performance compared to an existing algorithm. The potential applications of this work are manifold. The Hermite series based Spearman rank correlation estimator can be applied to fast and robust online calculation of correlation which may vary over time. Possible machine learning applications include, amongst others, fast feature selection and hierarchical clustering on massive data sets.

在本文中，我们描述了一种新的基于 Hermite 级数的 Spearman 秩相关系数的序列估计器，并提供了适用于平稳和非平稳设置的算法。为了处理非平稳设置，我们引入了一种新颖的、指数加权的 Spearman 秩相关估计器，它允许跟踪双变量数据流的局部非参数相关。据我们所知，这是第一个被提议用于估计不依赖于移动窗口方法的时变 Spearman 等级相关性的算法。我们通过真实数据和模拟研究探索基于 Hermite 级数的估计器的实际有效性，这些研究证明了良好的实际性能。与现有算法相比，模拟研究特别揭示了竞争性能。这项工作的潜在应用是多方面的。基于 Hermite 级数的 Spearman 等级相关性估计器可用于快速且稳健的相关性在线计算，相关性可能随时间而变化。可能的机器学习应用包括快速特征选择和海量数据集的层次聚类等。