Spearman秩相关的Hermite级数估计的序贯估计
Sequential estimation of Spearman rank correlation using Hermite series estimators
摘要：
在这篇文章中，我们描述了一个新的Hermite系列基于序贯估计斯皮尔曼秩相关系数，并提供算法适用于平稳和非平稳设置。为了处理非平稳设置，我们引入了一种新的，指数加权的斯皮尔曼秩相关估计，它允许跟踪的二元数据流的局部非参数相关。据我们所知，这是第一个算法提出估计时变斯皮尔曼秩相关，不依赖于移动窗口的方法。我们通过真实的数据和模拟研究，展示了良好的实际性能，探讨了厄米级数为基础的估计的实际有效性。特别是模拟研究揭示了竞争力的性能相比，现有的算法。这项工作的潜在应用是多方面的。基于Hermite级数的Spearman秩相关估计可用于快速、鲁棒的在线相关计算。可能的机器学习应用包括在海量数据集上的快速特征选择和分层聚类等。
英文摘要：
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.
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