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Sequential estimation of Spearman rank correlation using Hermite series estimators

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  • Stephanou, Michael
  • Varughese, Melvin

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.

Suggested Citation

  • Stephanou, Michael & Varughese, Melvin, 2021. "Sequential estimation of Spearman rank correlation using Hermite series estimators," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000610
    DOI: 10.1016/j.jmva.2021.104783
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    References listed on IDEAS

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    1. Michael Stephanou & Melvin Varughese, 2021. "On the properties of hermite series based distribution function estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 535-559, May.
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    7. Philippe Pébay & Timothy B. Terriberry & Hemanth Kolla & Janine Bennett, 2016. "Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights," Computational Statistics, Springer, vol. 31(4), pages 1305-1325, December.
    8. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
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