Computes the t* statistic corresponding to the tau star population coefficient introduced by Bergsma and Dassios (2014) <DOI:10.3150/13-BEJ514> and does so in O(n^2*log(n)) time following the algorithm of Weihs, Drton, and Leung (2016) <DOI:10.1007/s00180-015-0639-x>. Also allows for independence testing using the asymptotic distribution of t* as described by Nandy, Weihs, and Drton (2016) <http://arxiv.org/abs/1602.04387>. To directly compute the t* statistic see the function tStar. If otherwise interested in performing tests of independence then see the function tauStarTest.

Bergsma, Wicher; Dassios, Angelos. A consistent test of independence based
on a sign covariance related to Kendall's tau. *Bernoulli* 20 (2014), no.
2, 1006–1028.

Luca Weihs, Mathias Drton, and Dennis Leung. Efficient Computation of the
Bergsma-Dassios Sign Covariance. *Computational Statistics*, x:x-x,
2016. to appear.

Preetam Nandy, Luca Weihs, and Mathias Drton. Large-Sample Theory for the
Bergsma-Dassios Sign Covariance. arXiv preprint arXiv:1602.04387. 2016.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ```
## Not run:
library(TauStar)
# Compute t* for a concordant quadruple
tStar(c(1,2,3,4), c(1,2,3,4)) # == 2/3
# Compute t* for a discordant quadruple
tStar(c(1,2,3,4), c(1,-1,1,-1)) # == -1/3
# Compute t* on random normal iid normal data
set.seed(23421)
tStar(rnorm(4000), rnorm(4000)) # near 0
# Compute t* as a v-statistic
set.seed(923)
tStar(rnorm(100), rnorm(100), vStatistic=TRUE)
# Compute an approximation of tau* via resampling
set.seed(9492)
tStar(rnorm(10000), rnorm(10000),
resample=TRUE, sampleSize=30, numResamples=5000)
# Perform a test of independence using continuous data
set.seed(123)
x = rnorm(100)
y = rnorm(100)
testResults = tauStarTest(x,y)
print(testResults$pVal) # big p-value
# Now make x and y correlated so we expect a small p-value
y = y + x
testResults = tauStarTest(x,y)
print(testResults$pVal) # small p-value
## End(Not run)
``` |

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