testforDEP (version 0.2.0)

AUK: Draw Kendall plot and compute AUK.

Description

This function draws Kendall plot of 2 variables. Also provides an index AUK (area under Kendall plot).

Usage

AUK(x, y, plot = F, main = "Kendall plot", Auxiliary.line = T, BS.CI = 0, set.seed = FALSE)

Arguments

x

a numeric vector stores first variable.

y

a numeric vector stores second variable.

plot

a TRUE/ FALSE flag for generating Kendall plot or not.

main

a character indicating the title of the plot.

Auxiliary.line

a TRUE/ FALSE flag for drawing auxiliary lines or not.

BS.CI

a numeric specifying alpha for Bootstrap confidence interval. When euqal 0, confidence interval won't be computed.

set.seed

a TRUE/ FALSE flag specifying setting seed or not.

Value

a list containing a numeric AUK, a numeric vector W.in (x axis of plot), a numeric vector Hi.sort (y axis of plot), and three confidence intervals: normal CI, pivotal CI and percentage CI.

Details

AUK is bounded between 0 and 0.75. For positively correlated x and y's, say x = y, AUK = 0.75. And the plot follows the concave auxiliary line. While negatively correlated x and y's, AUK = 0. The plot is horizontal on y = 0. For independent x and y, AUK = 0.5. Kendall plot is on the diagonal. Due to possible variable overflow, this function is only suitable for input size less than 1000. Input size greater than 1000 causes error.

References

Vexler, Albert, Xiwei Chen, and Alan D. Hutson. "Dependence and independence: Structure and inference." Statistical methods in medical research (2015): 0962280215594198.

R package "VineCopula": Schepsmeier, Ulf, et al. "Package 'VineCopula'." (2015).

Examples

set.seed(123)
x = runif(100)
y = runif(100)

result = AUK(x, y, plot = TRUE)
result$AUK

#[1] 0.4987523