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Type: Package
Title: Inference for Optimal Transport
Version: 0.1.0
Imports: MASS (≥ 7.3-45), Rglpk (≥ 0.6-2), sm (≥ 2.2-5.4), transport (≥ 0.8-1)
Suggests: Rcplex (≥ 0.3.3)
Description: Sample from the limiting distributions of empirical Wasserstein distances under the null hypothesis and under the alternative. Perform a two-sample test on multivariate data using these limiting distributions and binning.
License: GPL-2
Encoding: UTF-8
RoxygenNote: 5.0.1
NeedsCompilation: no
Packaged: 2017-03-07 13:12:07 UTC; msommerfeld
Author: Max Sommerfeld [aut, cre]
Maintainer: Max Sommerfeld <max.sommerfeld@mathematik.uni-goettingen.de>
Repository: CRAN
Date/Publication: 2017-03-07 14:46:11

Two-sample test for multivariate data based on binning.

Description

Two-sample test for multivariate data based on binning.

Usage

binWDTest(x, y, L = 5, B = 100)

Arguments

x, y

The two samples, rows are realizations.

L

Number of bins in each dimension.

B

Number of realizations of limiting distribution to simulate.

Value

p-value.

Examples

## Not run: 
x <- MASS::mvrnorm(n = 100, mean = c(0, 0), Sigma = diag(1, 2))
y <- MASS::mvrnorm(n = 100, mean = c(0, 0), Sigma = diag(2, 2))
pVal <- binWDTest(x, y)
## End(Not run)

Sample from the limit distribution under the alternative.

Description

Sample from the limit distribution under the alternative.

Usage

limDisAlt(B = 1000, r, s, distMat, p = 1)

Arguments

B

Number of samples to generate.

r, s

Number of counts giving the two samples.

distMat

Distance matrix.

p

Cost exponent. Defaults to 1.

Value

A vector of samples.


m-out-of-n Bootstrap for the limiting distribution.

Description

m-out-of-n Bootstrap for the limiting distribution.

Usage

limDisAltBoot(r, s, distMat, B = 1000, p = 1, gamma = 0.9)

Arguments

r, s

Vectors of counts giving the two samples.

distMat

Distance matrix.

B

The number of samples to generate. Defaults to 1000.

p

Cost exponent. Defaults to 1.

gamma

m = n^gamma. Defaults to 0.9.

Value

A sample from the limiting distribution.


Sample from the limiting distribution under the null.

Description

Sample from the limiting distribution under the null.

Usage

limDisNull(B = 500, r, distMat, p = 1)

Arguments

B

number of samples to generate. Defaults to 500.

r

vector of probabilities in the original problem.

distMat

distance matrix in the original problem.

p

cost exponent. Defaults to 1.

Value

A vector of samples.


Sample from the limiting distribution under the null when the underlying space is a grid.

Description

Sample from the limiting distribution under the null when the underlying space is a grid.

Usage

limDisNullGrid(B = 500, r, p = 1)

Arguments

B

Number of bootstrap samples to generate. Defaults to 500.

r

vector of probabilities in the original problem. Is interpreted as a square matrix.

p

cost exponent.

Value

A vector of samples.


Compute the Wasserstein distance between to finite distributions.

Description

Compute the Wasserstein distance between to finite distributions.

Usage

wassDist(a, b, distMat, p = 1)

Arguments

a, b

Vectors representing probability distributions.

distMat

Cost matrix.

p

cost exponent.

Value

The Wasserstein distance.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.