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Kendallknight: An R package for efficient implementation of Kendall's correlation coefficient computation.

Mauricio Vargas Sepulveda^1,2

¹Munk School of Global Affairs and Public Policy, University of Toronto, Toronto, Ontario, Canada.

|June 18, 2025

Summary

The kendallknight package offers a faster way to compute Kendall's correlation coefficient for large datasets. This R package significantly reduces computation time while maintaining accuracy, benefiting statistical and econometric analyses.

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Area of Science:

Statistics and Econometrics
Computational Statistics

Background:

Kendall's rank correlation coefficient is a widely used non-parametric measure of statistical dependence.
Existing implementations can be computationally intensive, particularly for large datasets.
The need for efficient and accurate correlation coefficient computation is critical in data analysis.

Purpose of the Study:

To introduce the kendallknight package, an optimized implementation of Kendall's correlation coefficient.
To demonstrate significant performance improvements over standard implementations for large datasets.
To provide a robust and accurate tool for statistical and econometric applications.

Main Methods:

Development of an efficient algorithm for Kendall's tau computation based on Knight (1966) and subsequent literature.
Implementation within an R package (kendallknight) for accessibility.
Benchmarking against Base R's implementation using datasets of varying sizes.

Main Results:

The kendallknight package achieves drastic reductions in computation time, processing large datasets in milliseconds to minutes.
Performance gains are substantial, especially for large-scale data.
The implementation maintains high precision and handles edge cases and errors effectively.

Conclusions:

The kendallknight package offers a highly efficient and accurate solution for computing Kendall's correlation coefficient.
Its performance benefits make it particularly valuable for large-scale statistical and econometric analyses.
The package provides a practical advancement for researchers and practitioners requiring rapid correlation analysis.