dot-wassersteinTestSp: .wassersteinTestSp

In waddR: Statistical tests for detecting differential distributions based on the 2-Wasserstein distance

Description

Two-sample test to check for differences between two distributions (conditions) using the 2-Wasserstein distance: Semi-parametric implementation using a permutation test with a generalized Pareto distribution (GPD) approximation to estimate small p-values accurately

Usage

.wassersteinTestSp(x, y, permnum = 10000)

Arguments

x	univariate sample (vector) representing the distribution of condition A
y	univariate sample (vector) representing the distribution of condition B
permnum	number of permutations used in the permutation testing procedure

Details

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

Details concerning the permutation testing procedure with GPD approximation to estimate small p-values accurately can be found in Schefzik and Goncalves (2019).

Value

A vector concerning the testing results, precisely (see Schefzik and Goncalves (2019) 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 semi-parametric 2-Wasserstein distance-based test

• p.ad.gpd: in case the GPD fitting is performed: p-value of the Anderson-Darling test to check whether the GPD actually fits the data well (otherwise NA). NOTE: GPD fitting is currently not supported!

• N.exc: in case the GPD fitting is performed: number of exceedances (starting with 250 and iteratively decreased by 10 if necessary) that are required to obtain a good GPD fit (i.e. p-value of Anderson-Darling test greater or eqaul to 0.05) (otherwise NA) NOTE: GPD fitting is currently not supported!

• perc.loc: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• perc.size: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• perc.shape: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

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

References

Schefzik, R. and Goncalves, A. (2019).

waddR documentation built on Nov. 8, 2020, 8:32 p.m.