shiftedMMD {DRPT} | R Documentation |
A function computing an estimate of the shifted-MMD.
Description
A function computing the U-statistic (12). This serves as an estimator of the shifted-MMD defined in Section 3.2 of Bordino and Berrett (2025).
Usage
shiftedMMD(X, Y, r, kernel)
Arguments
X |
A numeric vector containing the first sample. |
Y |
A numeric vector containing the second sample. |
r |
A function specifying the hypothesised density ratio. |
kernel |
A function defining the kernel to be used for the U-statistic. |
Value
The value of the U-statistic (12).
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 = 250; m = 250; d = 2
r = function(x,y) {
return(4*x*y)
}
gaussian.kernel = function(x, y, lambda = 1){
return(lambda^(-d) * exp(-sum(((x - y) ^ 2) / (lambda ^ 2))))
}
X = as.matrix(cbind(runif(n, 0, 1), runif(n, 0, 1)))
Y = as.matrix(cbind(rbeta(m, 0.5, 0.3), rbeta(m, 0.5, 0.4)))
shiftedMMD(X,Y, r, gaussian.kernel)
[Package DRPT version 1.1 Index]