discreteT {DRPT}R Documentation

Compute test statistics for the DRPT in discrete settings.

Description

Computes the test statistics introduced in Bordino and Berrett (2025) for settings where the data support is discrete and finite.

Usage

discreteT(NX, NY, r, n, m, type = "V")

Arguments

NX

A vector of counts for the first sample. This corresponds to the sequence \mathrm{tot}_j - N_{Y,j}^p with p = \mathrm{id}, i.e. the identity permutation, as introduced in Section 2.1 of Bordino and Berrett (2025).

NY

A vector of counts for the second sample. This corresponds to the sequence N_{Y,j}^p with p = \mathrm{id}, i.e. the identity permutation, as introduced in Section 2.1 of Bordino and Berrett (2025).

r

A numeric vector of positive values specifying the hypothesised density ratio in the discrete setting.

n

The size of the first sample.

m

The size of the second sample.

type

A character string indicating which test statistic to compute. One of "U", "V", or "D". See the Details section for more information. Defaults to "V".

Details

When type = "U", the U-statistic (12) is calculated. When type = "V", the V-statistic (11) is computed. When type = "D", the test statistic (56) from Appendix B is returned.

Value

A numeric value representing the computed test statistic.

References

Bordino A, Berrett TB (2025). “Density Ratio Permutation Tests with connections to distributional shifts and conditional two-sample testing.” arXiv:2505.24529, https://arxiv.org/abs/2505.24529.

Examples

n = 100; m = n
X = sample(0:3, n, prob = c(1/4, 1/4, 1/4, 1/4), replace = TRUE)
Y = sample(0:3, m, prob = c(1/17, 3/17, 3/17, 10/17), replace = TRUE)
r = c(1, 3, 3, 10)

NX = table(X)
NY = table(Y)

discreteT(NX, NY, r, sum(NX), sum(NY), type = "V")
discreteT(NX, NY, r, sum(NX), sum(NY), type = "D")

[Package DRPT version 1.1 Index]