kerTests (version 0.1.4)

kertests: 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)

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.

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.

See Also

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