| Type: | Package |
| Title: | Generalized Kernel Two-Sample Tests |
| Version: | 0.1.4 |
| Author: | Hoseung Song [aut, cre], Hao Chen [aut] |
| Maintainer: | Hoseung Song <hosong@ucdavis.edu> |
| Description: | New kernel-based test and fast tests for testing whether two samples are from the same distribution. They work well particularly for high-dimensional data. Song, H. and Chen, H. (2023) <doi:10.48550/arXiv.2011.06127>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| NeedsCompilation: | no |
| Packaged: | 2023-08-22 20:14:00 UTC; hsong3 |
| Repository: | CRAN |
| Date/Publication: | 2023-08-22 20:40:02 UTC |
Generalized Kernel Two-Sample Tests
Description
This package can be used to determine whether two samples are from the same distribution. The Gaussian kernel with the median heuristic, which is the median of all pairwise distances among observations, is used. To obtain the median heuristic, the function med_sigma should be used. The main function is kertests
Author(s)
Hoseung Song and Hao Chen
Maintainer: Hoseung Song (hosong@ucdavis.edu)
References
Song, Hoseung, and Hao Chen (2020). Generalized kernel two-sample tests. arXiv:2011.06127
See Also
Examples
## Mean difference in Gaussian distribution.
d = 100
mu = 0.2
sam = 100
n = 200
set.seed(500)
X = matrix(rnorm(d*sam), sam)
Y = matrix(rnorm(d*sam,mu), sam)
sigma = med_sigma(X, Y) # median heuristic
a = kertests(X, Y, sigma, r1=1.2, r2=0.8, perm=1000)
# output results based on the permutation and the asymptotic results
# the test statistic values can be found in a$teststat
# p-values can be found in a$pval
Generalized Kernel Two-Sample Tests
Description
This function provides generalzied kernel-based two-sample tests.
Usage
kertests(X, Y, sigma, r1=1.2, r2=0.8, perm=0)
Arguments
X |
The first samples. |
Y |
The second samples. |
sigma |
The bandwidth of Gaussian kernels. The median heuristic should be used. |
r1 |
The constant in the test statistics |
r2 |
The constant in the test statistics |
perm |
The number of permutations performed to calculate the p-value of the test. The default value is 0, which means the permutation is not performed and only approximated p-value based on the asymptotic theory is provided. Doing permutation could be time consuming, so be cautious if you want to set this value to be larger than 10,000. |
Value
Returns a list teststat with each test statistic value and a list pval with p-values of the tests. See below for more details.
GPK |
The value of the test statistic GPK |
ZW1 |
The value of the test statistic |
ZW2 |
The value of the test statistic |
ZD |
The value of the test statistic |
fGPK_appr |
The approximated p-value of fGPK based on asymptotic theory. |
fGPKM_appr |
The approximated p-value of |
fGPK_Simes_appr |
The approximated p-value of fGPK based on asymptotic theory with a Simes procedure. |
fGPKM_Simes_appr |
The approximated p-value of |
GPK_perm |
The permutation p-value of GPK when argument ‘perm’ is positive. |
fGPK_perm |
The permutation p-value of fGPK when argument ‘perm’ is positive. |
fGPKM_perm |
The permutation p-value of |
fGPK_Simes_perm |
The permutation p-value of fGPK with a Simes procedure when argument ‘perm’ is positive. |
fGPKM_Simes_perm |
The permutation p-value of |
See Also
Examples
## Mean difference in Gaussian distribution.
d = 100
mu = 0.2
sam = 100
n = 200
set.seed(500)
X = matrix(rnorm(d*sam), sam)
Y = matrix(rnorm(d*sam,mu), sam)
sigma = med_sigma(X, Y) # median heuristic
a = kertests(X, Y, sigma, r1=1.2, r2=0.8, perm=1000)
# output results based on the permutation and the asymptotic results
# the test statistic values can be found in a$teststat
# p-values can be found in a$pval
Compute the Median Heuristic
Description
This function provides the most popular bandwidth of the Gaussian kernel, the median heuristic.
Usage
med_sigma(X, Y)
Arguments
X |
The first samples. |
Y |
The second samples. |
Value
Returns a numeric value, the median heuristic, which is the median of all pairwise distances among pooled observations, as a bandwidth of the kernel.
See Also
Examples
## Mean difference in Gaussian distribution.
d = 100
mu = 0.2
sam = 100
n = 200
set.seed(500)
X = matrix(rnorm(d*sam), sam)
Y = matrix(rnorm(d*sam,mu), sam)
sigma = med_sigma(X, Y) # median heuristic (bandwidth)