ComparePowerOneSampleCTest {FuzzyResampling}

Comparison of the resampling approaches based on the power for the one-sample test for the mean.

Description

ComparePowerOneSampleCTest returns the percentage of rejections for the one-sample C-test when different resampling methods are used.

Usage

ComparePowerOneSampleCTest(
  generator,
  mu_0,
  shiftVector,
  sampleSize = 10,
  numberOfSamples = 10,
  initialSamples = 100,
  theta = 1/3,
  significance = 0.05,
  ...
)

Arguments

generator

Name of the generator for sampling initial samples. For the possible names check the values of samplingGenerators vector.

mu_0

Triangular or trapezoidal fuzzy number which is used for the null hypothesis of the C-test.

shiftVector

Deterministic vector of shifts that are sequentially added to all initial samples.

sampleSize

Size of the single initial sample.

numberOfSamples

Number of the bootstrapped samples used to estimate the p-value.

initialSamples

Number of the generated initial samples. More than one value can be given in the form of matrix.

theta

The weighting parameter for the mid/spread distance applied in the C-test.

significance

The significance value used to accept/reject the hypothesis for the one-sample C-test.

...

Parameters which are passed to OneSampleCTest or the respective generator

Details

The function generates a sequence of initial samples (their number is given in initialSamples, the size is determined by sampleSize) for fuzzy numbers of the type specified by generator. Then a sequence of deterministic shifts described by vector shiftVector is added to each fuzzy observation in these samples. Next, function OneSampleCTest is executed to calculate the p-value for each combination of the initial sample and resampling method. Then, by comparing the p-value with the assumed significance level significance we make a decision whether to reject the null hypothesis for the one-sample C-test for the mean (see Lubiano et al. (2016)) or not. The output of this procedure is the percentage of rejections as a function of values from shiftVector.

Value

This function returns a matrix of percentage of rejections for the one-sample C-test for the mean. Rows in this matrix are related to the values from shiftVector, and the columns - to all resampling methods.

References

Lubiano, M.A., Montenegro M., Sinova, B., de Saa, S.R., Gil, M.A. (2016) Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications European Journal of Operational Research, 251, pp. 918-929

See Also

ComparisonSEMean for the comparison of resampling methods based on SE/MSE for the mean, ComparisonOneSampleCTest for the comparison of resampling methods based on power for the one-sample C-test for the mean.

Other comparison of resampling methods: ComparisonOneSampleCTest(), ComparisonSEMean()

Examples

## Not run: 

# seed PRNG

set.seed(1234)

# compare the resampling methods for the synthetic data generated using GeneratorNU function
# and two values of the shifts

ComparePowerOneSampleCTest("GeneratorNU",mu_0 = c(-0.4,-0.1,0.1,0.4), shiftVector = c(0,0.5),
mu = 0, sigma = 1, a = 0.2, b = 0.6)
## End(Not run)