# kertests: Generalized Kernel Two-Sample Tests In kerTests: Generalized Kernel Two-Sample Tests

 kertests R Documentation

## 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 `\textrm{Z}_{W,r1}`. `r2` The constant in the test statistics `\textrm{Z}_{W,r2}`. `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 `\textrm{Z}_{W,r1}`. `ZW2` The value of the test statistic `\textrm{Z}_{W,r2}`. `ZD` The value of the test statistic `\textrm{Z}_{D}`. `fGPK_appr` The approximated p-value of fGPK based on asymptotic theory. `fGPKM_appr` The approximated p-value of `\textrm{fGPK}_{M}` based on asymptotic theory. `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 `\textrm{fGPK}_{M}` based on asymptotic theory with a Simes procedure. `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 `\textrm{fGPK}_{M}` when argument ‘perm’ is positive. `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 `\textrm{fGPK}_{M}` with a Simes procedure when argument ‘perm’ is positive.

`kerTests-package`, `med_sigma`

### 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

``````

kerTests documentation built on Aug. 23, 2023, 1:09 a.m.