tStar: Computing t*

In SONGDONGYUAN1994/PseudotimeDE: Inference of differential gene expression along cell pseudotime with well-calibrated p-values from single-cell RNA sequencing data

Computing t*

Description

Computes the t* U-statistic for input data pairs (x_1,y_1), (x_2,y_2), ..., (x_n,y_n) using the algorithm developed by Heller and Heller (2016) <arXiv:1605.08732> building off of the work of Weihs, Drton, and Leung (2015) <DOI:10.1007/s00180-015-0639-x>.

Usage

tStar(x, y)

Arguments

x	A numeric vector of x values (length >= 4).
y	A numeric vector of y values, should be of the same length as x.

Value

The numeric value of the t* statistic.

References

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.

Heller, Yair and Heller, Ruth. "Computing the Bergsma Dassios sign-covariance." arXiv preprint arXiv:1605.08732 (2016).

Weihs, Luca, Mathias Drton, and Dennis Leung. "Efficient Computation of the Bergsma-Dassios Sign Covariance." arXiv preprint arXiv:1504.00964 (2015).

Examples

## 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)

## End(Not run)

SONGDONGYUAN1994/PseudotimeDE documentation built on Jan. 23, 2025, 7:15 a.m.