README.md

In chaim-e/independence: Fast Rank-Based Independence Testing

independence (R package)

Fast Rank-Based Independence Tests

Performs three ranking-based nonparametric tests for the independence of two continuous variables: (1) the classical Hoeffding's D test; (2) a refined variant of it, named R; (3) the Bergsma-Dassios T sign covariance. The first test is consistent assuming an absolutely continuous bivariate distribution, i.e., the population coefficient D=0 iff the variables are independent. The latter two are consistent under no restriction on the distribution. All three statistics are computed in time O(n log n) given n iid paired samples. The computation of R and T uses a new algorithm, following work of Even-Zohar and Leng (2019), see https://arxiv.org/abs/2010.09712 and references therein.

Install

From CRAN

install.packages("independence")
library(independence)

From GitHub

library(devtools)
install_github("chaim-e/independence")
library(independence)

Examples

tau.star.test(rnorm(1000000),rnorm(1000000))
hoeffding.D.test(rnorm(1000000),rnorm(1000000))
hoeffding.refined.test(rnorm(1000000),rnorm(1000000))

Why you should use the refined Hoeffding's D or tau*

Example (I)

set.seed(12345)
f <- function(a,b) ifelse(a>b, pmin(b,a/2), pmax(b,(a+1)/2))
x <- runif(300)
y <- f(x, runif(300))
hoeffding.D.test(x,y)$p.value
# [1] 0.4589397
hoeffding.refined.test(x,y)$p.value
# [1] 2.138784e-10
tau.star.test(x,y)$p.value
# [1] 1.053099e-08

Example (II)

set.seed(13579)
f <- function(a,b) ifelse(a>0.5, pmin(b,1-0.5/a), pmax(b,0.5/(1-a)))
x <- runif(50)
y <- f(x, runif(50))
hoeffding.D.test(x,y)$p.value
# [1] 0.4157275
hoeffding.refined.test(x,y)$p.value
# [1] 8.04458e-08
tau.star.test(x,y)$p.value
# [1] 1.009128e-05

Example (III)

set.seed(54321)
f <- function(a,b) (a+b-b%%(2^ceiling(log(pmin(a,1-a),2))))%%1
x <- runif(1000)
y <- f(x, runif(1000))
hoeffding.D.test(x,y)$p.value
# [1] 0.5391983
hoeffding.refined.test(x,y)$p.value
# [1] 6.539453e-09
tau.star.test(x,y)$p.value
# [1] 8.865218e-07

chaim-e/independence documentation built on Oct. 31, 2020, 10:11 a.m.