dot-wassersteinTestAsy: Asymptotic theory-based test using the 2-Wasserstein distance...

.wassersteinTestAsyR Documentation

Asymptotic theory-based test using the 2-Wasserstein distance to check for differential distributions

Description

Two-sample test to check for differences between two distributions using the 2-Wasserstein distance: Implementation using a test based on asymptotic theory

Usage

.wassersteinTestAsy(x, y)

Arguments

x

sample (vector) representing the distribution of condition A

y

sample (vector) representing the distribution of condition B

Details

This is the asymptotic version of wasserstein.test, for the semi-parametric procedure see .wassersteinTestSp.

Details concerning the testing procedure based on asymptotic theory can be found in Schefzik et al (2020).

Note that the asymptotic theory-based test should only be employed when the two samples x and y can be assumed to come from continuous distributions.

Value

A vector of 13, see Schefzik et al. (2020) for details:

  • d.wass: 2-Wasserstein distance between the two samples computed by quantile approximation

  • d.wass^2: squared 2-Wasserstein distance between the two samples computed by quantile approximation

  • d.comp^2: squared 2-Wasserstein distance between the two samples computed by decomposition approximation

  • d.comp: 2-Wasserstein distance between the two samples computed by decomposition approximation

  • location: location term in the decomposition of the squared 2-Wasserstein distance between the two samples

  • size: size term in the decomposition of the squared 2-Wasserstein distance between the two samples

  • shape: shape term in the decomposition of the squared 2-Wasserstein distance between the two samples

  • rho: correlation coefficient in the quantile-quantile plot

  • pval: p-value of the 2-Wasserstein distance-based test using asymptotic theory

  • perc.loc: fraction (in %) of the location part with respect to the overall squared 2-Wasserstein distance obtained by the decomposition approximation

  • perc.size: fraction (in %) of the size part with respect to the overall squared 2-Wasserstein distance obtained by the decomposition approximation

  • perc.shape: fraction (in %) of the shape part with respect to the overall squared 2-Wasserstein distance obtained by the decomposition approximation

  • decomp.error: relative error between the squared 2-Wasserstein distance obtained by the quantile approximation and the squared 2-Wasserstein distance obtained by the decomposition approximation

References

Schefzik, R., Flesch, J., and Goncalves, A. (2020). waddR: Using the 2-Wasserstein distance to identify differences between distributions in two-sample testing, with application to single-cell RNA-sequencing data.


goncalves-lab/waddR documentation built on June 29, 2023, 12:18 a.m.