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

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.