independence (version 1.0.1)

independence: independence

Description

Fast Rank-Based Independence Testing

Details

The package independence provides three ranking-based nonparametric tests for the independence of two continuous variables X and Y:

1. the classical Hoeffding's D test: hoeffding.D.test

2. a refined variant of it, named R: hoeffding.refined.test

3. the Bergsma-Dassios T* sign covariance: tau.star.test

The first test is consistent assuming an absolutely continuous joint distribution, i.e., the population coefficient D=0 iff the variables are independent. The latter two are consistent under no restriction on the distribution.

Given an iid sample (X1,Y1),...,(Xn,Yn), all three statistics are computed in time O(n log n) improving upon previous implementations. The statistics R and T* are computed by a new algorithm, following work of Even-Zohar and Leng. It is based on the fast counting of certain patterns in the permutation that relates the ranks of X and Y. See [arxiv:2010.09712] and references therein.

See Also

tau.star.test, hoeffding.D.test, hoeffding.refined.test relative.order

Examples

# NOT RUN {
library(independence)

## independent
set.seed(123)
xs = rnorm(10000)
ys = rnorm(10000)
hoeffding.D.test(xs,ys)
hoeffding.refined.test(xs,ys)
tau.star.test(xs,ys)

## dependent, even though uncorrelated
set.seed(123)
xs = rnorm(10000,0,3001:13000)
ys = rnorm(10000,0,3001:13000)
hoeffding.D.test(xs,ys)
hoeffding.refined.test(xs,ys)
tau.star.test(xs,ys)

## dependent but not absolutely continuous, fools Hoeffding's D
set.seed(123)
xs = runif(200)
f = function(x,y) ifelse(x>y, pmin(y,x/2), pmax(y,(x+1)/2))
ys = f(xs,runif(200))
hoeffding.D.test(xs,ys)
hoeffding.refined.test(xs,ys)
tau.star.test(xs,ys)

# }