Description Usage Arguments Details Value References

Two-sample test to check for differences between two distributions 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

1 | ```
.wassersteinTestSp(x, y, permnum = 10000)
``` |

`x` |
sample (vector) representing the distribution of
condition |

`y` |
sample (vector) representing the distribution of
condition |

`permnum` |
number of permutations used in the permutation testing procedure |

This is the semi-parametric version of `wasserstein.test`

, for the
asymptotic theory-based procedure see `.wassersteinTestAsy`

.

Details concerning the permutation testing procedure with GPD approximation to estimate small p-values accurately can be found in Schefzik et al. (2020).

A vector of 15, 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 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).

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

*≥q 0.05*(otherwise NA).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

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.

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