Kendall Correlation

Description

coefficient between two numeric vectors. It uses the algorithm described in Knight (1966), which is based on the number of concordant and discordant pairs. The computational complexity of the algorithm is \(O(n \log(n))\), which is faster than the base R implementation in stats::cor(..., method = "kendall") that has a computational complexity of \(O(n^2)\). For small vectors (i.e., less than 100 observations), the time difference is negligible. However, for larger vectors, the difference can be substantial.

By construction, the implementation drops missing values on a pairwise basis. This is the same as using stats::cor(..., use = "pairwise.complete.obs").

Arguments

Return

A numeric value between -1 and 1.

Examples

# input vectors -> scalar output
x <- c(1, 0, 2)
y <- c(5, 3, 4)
kendall_cor(x, y)

## [1] 0.3333333

# input matrix -> matrix output
x <- mtcars[, c("mpg", "cyl")]
kendall_cor(x)

##            [,1]       [,2]
## [1,]  1.0000000 -0.7953134
## [2,] -0.7953134  1.0000000

References

Kendall's Tau with Ungrouped Data". Journal of the American Statistical Association, 61(314), 436–439.

Abrevaya J. (1999). Computation of the Maximum Rank Correlation Estimator. Economic Letters 62, 279-285.

Christensen D. (2005). Fast algorithms for the calculation of Kendall's Tau. Journal of Computational Statistics 20, 51-62.

Emara (2024). Khufu: Object-Oriented Programming using C++