Package '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)

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.

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

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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 ([email protected])

References

Song, Hoseung, and Hao Chen (2020). Generalized kernel two-sample tests. arXiv:2011.06127

See Also

kertests, 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

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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

kerTests-package, kertests

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)

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