The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.
The two-sample test can be additionally performed by providing the
two samples to be compared as x
and y
. We
generate the sample \(y = (y_1,
\ldots,y_n)\) from a skew-normal distribution \(SN_d(0,I_d, \lambda)\), where \(d=4\), \(n=200\) and \(\lambda= (0.5,\ldots,0.5)\).
library(sn)
library(mvtnorm)
library(QuadratiK)
n <- 200
d <- 4
skewness_y <- 0.5
set.seed(2468)
x_2 <- rmvnorm(n, mean = rep(0,d))
y_2 <- rmsn(n=n, xi=0, Omega = diag(d), alpha=rep(skewness_y,d))
##
## Kernel-based quadratic distance two-sample test
## U-statistics Dn Trace
## ------------------------------------------------
## Test Statistic: 4.276823 9.843008
## Critical Value: 0.7745576 1.783123
## H0 is rejected: TRUE TRUE
## CV method: subsampling
## Selected tuning parameter h: 2
For the two-sample case, the summary
function provides
the results from the test and the descriptive statistics per variable
and per group, as similarly described for the \(k\)-sample test. Additionally, it generates
the qq-plots comparing the quantiles of the two groups for each
variable.
##
## Kernel-based quadratic distance two-sample test
## Statistic Test_Statistic Critical_Value Reject_H0
## 1 Dn 4.276823 0.7745576 TRUE
## 2 Trace 9.843008 1.7831227 TRUE
## [[1]]
## Group 1 Group 2 Overall
## mean 0.021762263 0.3799990 0.2008806
## sd 1.014655344 0.9498167 0.9977884
## median -0.005110155 0.3833061 0.2125618
## IQR 1.471877262 1.1310211 1.3666010
## min -2.675477796 -2.2219439 -2.6754778
## max 2.300153117 3.1690406 3.1690406
##
## [[2]]
## Group 1 Group 2 Overall
## mean -0.03347117 0.2216529 0.09409085
## sd 1.06408749 1.0304067 1.05383755
## median 0.02476594 0.1717768 0.09272994
## IQR 1.52458343 1.3739349 1.45668193
## min -3.22222061 -2.6162342 -3.22222061
## max 2.96751758 2.3300745 2.96751758
##
## [[3]]
## Group 1 Group 2 Overall
## mean -0.06473408 0.3312699 0.1332679
## sd 0.93818786 0.9868499 0.9818422
## median -0.07044427 0.4006745 0.1382735
## IQR 1.37135831 1.2185714 1.3854150
## min -2.86000669 -3.0246026 -3.0246026
## max 2.56476485 2.7590501 2.7590501
##
## [[4]]
## Group 1 Group 2 Overall
## mean -0.1658894 0.2065222 0.02031639
## sd 1.0175325 0.9718613 1.01104987
## median -0.2371959 0.1427746 0.04889195
## IQR 1.3802070 1.2320445 1.32957715
## min -2.5899601 -2.0159679 -2.58996007
## max 2.7066430 2.6637589 2.70664302
The figure automatically generated by the summary
function on the result of the two-sample test displays the qq-plots
between the two samples with a table of the standard descriptive
statistics for each variable, computed per group and overall.
If a value of \(h\) is not provided,
the function automatically performs the function
select_h
.
For a more accurate search of the tuning parameter, the function
select_h
can be used. This function needs the input
x
and y
as the function kb.test
for the two-sample problem.
The functionselect_h
will also generate a figure which
displays the obtained power versus the considered \(h\), for the alternatives \(\delta\).
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.