Statistical Inference via Lancaster Correlation

Implementation of the methods described in Holzmann, Klar (2024) . Lancaster correlation is a correlation coefficient which equals the absolute value of the Pearson correlation for the bivariate normal distribution, and is equal to or slightly less than the maximum correlation coefficient for a variety of bivariate distributions. Rank and moment-based estimators and corresponding confidence intervals are implemented, as well as independence tests based on these statistics.

lancor: Statistical Inference via Lancaster Correlation

Synopsis

The lancor package implements the methods described in Holzmann, Klar (2024). Lancaster correlation is a correlation coefficient which equals the absolute value of the Pearson correlation for the bivariate normal distribution, and is equal to or slightly less than the maximum correlation coefficient for a variety of bivariate distributions. Rank and moment-based estimators and corresponding confidence intervals are implemented, as well as independence tests based on these statistics.

Examples

The Lancaster correlation coefficient and the linear Lancaster correlation coefficient are estimated via the lcor function:

n <- 1000 
x <- matrix(rnorm(n*2), n)
lcor(x, type = "rank")
lcor(x, type = "linear")

Confidence intervals are given by the lcor.ci function:

 n <- 1000
 x <- matrix(rnorm(n*2), n)
 nu <- 2
 y <- x / sqrt(rchisq(n, nu)/nu)
 lcor(y, type = "rank")
 lcor.ci(y, type = "rank")

Finally the Lancaster correlation test of bivariate independence lcor.test:

 n <- 200
 x <- matrix(rnorm(n*2), n)
 nu <- 2
 y <- x / sqrt(rchisq(n, nu)/nu)
 cor.test(y[,1], y[,2], method = "spearman")
 lcor.test(y, type = "rank") 

Installation via CRAN

The lancor package can be installed from within R via

install.packages("lancor")

Authors

Hajo Holzmann, Bernhard Klar

License

GPL-2