m_test_statistic

<code>m_test_statistic</code> calculates the test statistics for
tests based on M-estimators.

Implementations of several robust nonparametric two-sample tests
for location or scale differences. The test statistics are based on robust
location and scale estimators, e.g. the sample median or the Hodges-Lehmann estimators
as described in Fried & Dehling (2011) <doi:10.1007/s10260-011-0164-1>.
The p-values can be computed via the permutation principle, the randomization principle, or by using
the asymptotic distributions of the test statistics under the null hypothesis, which ensures
(approximate) distribution independence of the test decision. To test for a difference in
scale, we apply the tests for location difference to transformed observations; see Fried (2012) <doi:10.1016/j.csda.2011.02.012>.
Random noise on a small range can be added to the original observations in order to
hold the significance level on data from discrete distributions.
The location tests assume homoscedasticity and the scale tests require the
location parameters to be zero.

Sermad Abbas

robnptests

Robust Nonparametric Two-Sample Tests for Location/Scale

Barbara Brune

Roland Fried

m_test_statistic function

<dl><dt>x</dt>
<dd>a (non-empty) numeric vector of data values.</dd>
<dt>y</dt>
<dd>a (non-empty) numeric vector of data values.</dd>
<dt>psi</dt>
<dd>kernel used for optimization.
Must be one of <code>"bisquare"</code>, <code>"hampel"</code> and <code>"huber"</code>.
The default is <code>"huber"</code>.</dd>
<dt>k</dt>
<dd>tuning parameter(s) for the respective kernel function,
defaults to parameters implemented in <code>.Mpsi.tuning.default(psi)</code>
in the package <a href="https://cran.r-project.org/package=robustbase">robustbase</a>.</dd>
<dt>...</dt>
<dd>additional arguments <code>c1</code> and <code>c2</code> that can be passed to
the function <code>scaleTau2()</code>, which is used internally for
estimating the within-sample dispersion, in order to account for
non-normal distributions; see MarZam02robu;textualrobnptests.</dd></dl>

Arguments

Test statistics for the M-tests — m_test_statistic

<dl>

<dt>x</dt>
<dd>a (non-empty) numeric vector of data values.</dd>


<dt>y</dt>
<dd>a (non-empty) numeric vector of data values.</dd>


<dt>psi</dt>
<dd>kernel used for optimization.
Must be one of <code>"bisquare"</code>, <code>"hampel"</code> and <code>"huber"</code>.
The default is <code>"huber"</code>.</dd>


<dt>k</dt>
<dd>tuning parameter(s) for the respective kernel function,
defaults to parameters implemented in <code>.Mpsi.tuning.default(psi)</code>
in the package <a href='https://cran.r-project.org/package=robustbase'>robustbase</a>.</dd>


<dt>...</dt>
<dd>additional arguments <code>c1</code> and <code>c2</code> that can be passed to
the function <code>scaleTau2()</code>, which is used internally for
estimating the within-sample dispersion, in order to account for
non-normal distributions; see MarZam02robu;textualrobnptests.</dd>

</dl>

m_test_statistic: Test statistics for the M-tests

Description

Usage

Value

Arguments

Details

Examples