bosfr (Bounds of Spearman’s Footrule)

bosfr computes exact bounds of Spearman’s footrule in the presence of missing data, and performs independence test based on the bounds with controlled Type I error regardless of the values of missing data. Note this package is suitable only for univariate distinct data where no ties is allowed. Bounds of Kendall’s tau is also available with missing data, provided the bounds of Spearman’s footrule. See Zeng et al., 2025 for more details.

Installation

You can install the development version of bosfr from GitHub with:

# install.packages("devtools")
devtools::install_github("Yijin-Zeng/bosfr-R-package")

Example

There are some basic examples which shows you how to use this package:

library(bosfr)
### compute exact bounds of Spearman's footrule between incomplete ranked lists
X <- c(1, 2, NA, 4, 3)
Y <- c(3, NA, 4, 2, 1)
boundsSFR(X, Y, pval=FALSE)
#> $bounds
#> [1]  6 12
#> 
#> $bounds.scaled
#> [1] -0.50  0.25

### compute exact bounds of Spearman's footrule between incomplete vectors of distinct data

X <- c(1.3, 2.6, NA, 4.2, 3.5)
Y <- c(5.5, NA, 6.5, 2.6, 1.1)
boundsSFR(X, Y, pval=TRUE)
#> $bounds
#> [1]  6 12
#> 
#> $bounds.scaled
#> [1] -0.50  0.25
#> 
#> $pvalue
#> [1] 1
#> 
#> $bounds.pvalue
#> [1] 0.1197949 1.0000000

### Compute bounds of Kendall's tau
X <- c(1, 2, NA, 4, 3)
Y <- c(3, NA, 4, 2, 1)
boundsKendall(X, Y)
#> $bounds
#> [1]  3 12
#> 
#> $bounds.scaled
#> [1] -1.0  0.4

References

Zeng Y., Adams N.M., Bodenham D.A. Exact Bounds of Spearman’s footrule in the Presence of Missing Data with Applications to Independence Testing. arXiv preprint arXiv:2501.11696. 2025 Jan 20.