ComparisonSEMean

<code>ComparisonSEMean</code> estimates the standard error (SE) or the mean-squared error (MSE) for the mean for
all resampling approaches.

The classical (i.e. Efron's, see Efron and Tibshirani (1994, ISBN:978-0412042317) "An Introduction to the Bootstrap") bootstrap is widely used for both the real (i.e. "crisp") and fuzzy data.
The main aim of the algorithms implemented in this package is to overcome a problem with repetition of a few distinct values and to create fuzzy numbers, which are "similar" (but not the same) to values from the initial sample.
To do this, different characteristics of triangular/trapezoidal numbers are kept (like the value, the ambiguity, etc., see Grzegorzewski et al. <doi:10.2991/eusflat-19.2019.68>, Grzegorzewski et al. (2020) <doi:10.2991/ijcis.d.201012.003>, Grzegorzewski et al. (2020) <doi:10.34768/amcs-2020-0022>, Grzegorzewski and Romaniuk (2022) <doi:10.1007/978-3-030-95929-6_3>, Romaniuk and Hryniewicz (2019) <doi:10.1007/s00500-018-3251-5>).
Some additional procedures related to these resampling methods are also provided,
like calculation of the Bertoluzza et al.'s distance (aka the mid/spread distance, see Bertoluzza et al. (1995) "On a new class of distances between fuzzy numbers")
and estimation of the p-value of the one- and two- sample bootstrapped test for the mean (see Lubiano et al. (2016, <doi:10.1016/j.ejor.2015.11.016>)).
Additionally, there are procedures which randomly generate trapezoidal fuzzy numbers using some well-known statistical distributions.

Maciej Romaniuk

FuzzyResampling

Resampling Methods for Triangular and Trapezoidal Fuzzy Numbers

Przemyslaw Grzegorzewski

Olgierd Hryniewicz

ComparisonSEMean function

<dl><dt>generator</dt>
<dd>Name of the generator for sampling initial samples.
For the possible names check the values of <code>samplingGenerators</code> vector.</dd>
<dt>sampleSize</dt>
<dd>Size of the single initial sample.</dd>
<dt>numberOfSamples</dt>
<dd>Number of the initial samples.</dd>
<dt>repetitions</dt>
<dd>Number of the secondary samples which are created using the selected resampling method.</dd>
<dt>trueMean</dt>
<dd>If the value is given, then the mean-squared error (MSE) is calculated for this value and the means of the bootstrapped
samples. Otherwise, the standard error (SE) is calculated based on the overall mean of the secondary samples.</dd>
<dt>theta</dt>
<dd>The weighting parameter for the mid/spread distance applied in the C-test.</dd>
<dt>...</dt>
<dd>Parameters which are passed to <code>SEResamplingMean</code> or the respective <code>generator</code></dd></dl>

Arguments

Comparison of the resampling approaches based on the SE/MSE for the mean. — ComparisonSEMean

<dl>

<dt>generator</dt>
<dd>Name of the generator for sampling initial samples.
For the possible names check the values of <code>samplingGenerators</code> vector.</dd>


<dt>sampleSize</dt>
<dd>Size of the single initial sample.</dd>


<dt>numberOfSamples</dt>
<dd>Number of the initial samples.</dd>


<dt>repetitions</dt>
<dd>Number of the secondary samples which are created using the selected resampling method.</dd>


<dt>trueMean</dt>
<dd>If the value is given, then the mean-squared error (MSE) is calculated for this value and the means of the bootstrapped
samples. Otherwise, the standard error (SE) is calculated based on the overall mean of the secondary samples.</dd>


<dt>theta</dt>
<dd>The weighting parameter for the mid/spread distance applied in the C-test.</dd>


<dt>...</dt>
<dd>Parameters which are passed to <code>SEResamplingMean</code> or the respective <code>generator</code></dd>

</dl>

ComparisonSEMean: Comparison of the resampling approaches based on the SE/MSE for the mean.

Description

Usage

Value

Arguments

Details

References

See Also

Examples