Sequential estimation of Spearman rank correlation using Hermite series estimators

TL;DR

This paper introduces a novel Hermite series based sequential estimator for the Spearman rank correlation, capable of handling both stationary and non-stationary data streams, with practical algorithms and demonstrated effectiveness.

Contribution

It presents the first non-window-based algorithm for time-varying Spearman correlation estimation using Hermite series, including a new exponentially weighted estimator for non-stationary data.

Findings

Good practical performance demonstrated through real data and simulations

Competitive results compared to existing algorithms

Effective in both stationary and non-stationary settings

Abstract

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.