EpistemicEstimator {FuzzySimRes}

Apply the epistemic bootstrap to find an estimator.

Description

'EpistemicEstimator' calculates the selected estimator and its SE/MSE for the fuzzy sample using the epistemic bootstrap approach.

Usage

EpistemicEstimator(
  fuzzySample,
  estimator = "sd",
  cutsNumber = 1,
  bootstrapMethod = "std",
  trueValue = NA,
  ...
)

Arguments

fuzzySample

Sample of fuzzy numbers (given in the form of a list or as a single number) or a matrix with already sampled values (i.e. output of function AntitheticBootstrap or EpistemicBootstrap).

estimator

Real-valued function used to calculate the respective estimator.

cutsNumber

Number of cuts used in the epistemic bootstrap.

bootstrapMethod

The standard (std) or antithetic (anti) method used for the epistemic bootstrap.

trueValue

The true (usually unknown) value of the estimated parameter. If value other than NA is used, then the MSE is calculated.

...

Possible parameters passed to other functions.

Details

For the initial sample given by fuzzySample, the function calculates the selected estimator (provided by the respective function as the estimator parameter) using the standard (if bootstrapMethod is set to "std") or the antithetic (when bootstrapMethod="anti") epistemic bootstrap. The initial sample should be given in the form of a list of numbers or a single number. These values have to be the fuzzy numbers defined as in the FuzzyNumbers package. The estimators are calculated for each epistemic bootstrap sample (i.e. based on the rows of the output matrix), then these values are averaged to give the final output (i.e. the mean for all cuts is obtained).

If, instead of fuzzy sample, the matrix is given by the parameter fuzzySample, then this matrix is treated as the direct output from the epistemic or the antithetic bootstrap. Then, the respective estimator is directly calculated.

Additionally, the standard error (SE) of this estimator is calculated and its mean squared error (MSE). This second type of the error is used if some value (other than NA) is provided for the trueValue parameter.

Value

The output is given in the form of a list consisting of real numbers: value - the obtained estimator, SE - its SE, and MSE - its MSE.

References

Grzegorzewski, P., Romaniuk, M. (2022) Bootstrap Methods for Epistemic Fuzzy Data. International Journal of Applied Mathematics and Computer Science, 32(2)

Grzegorzewski, P., Romaniuk, M. (2022) Bootstrapped Kolmogorov-Smirnov Test for Epistemic Fuzzy Data. Communications in Computer and Information Science, CCIS 1602, pp. 494-507, Springer

Gagolewski, M., Caha, J. (2021) FuzzyNumbers Package: Tools to deal with fuzzy numbers in R. R package version 0.4-7, https://cran.r-project.org/web/packages=FuzzyNumbers

See Also

EpistemicMean for the epistemic estimator of the mean, EpistemicCorrectedVariance for the corrected epistemic estimator of the variance

Examples

# seed PRNG

set.seed(1234)

# generate an initial fuzzy sample

list1<-SimulateSample(20,originalPD="rnorm",parOriginalPD=list(mean=0,sd=1),
incrCorePD="rexp", parIncrCorePD=list(rate=2),
suppLeftPD="runif",parSuppLeftPD=list(min=0,max=0.6),
suppRightPD="runif", parSuppRightPD=list(min=0,max=0.6),
type="trapezoidal")



# calculate the standard deviation using the standard epistemic bootstrap approach

EpistemicEstimator(list1$value,estimator="sd",cutsNumber = 30)

# calculate the median using the antithetic epistemic bootstrap approach

EpistemicEstimator(list1$value,estimator="median",cutsNumber = 30,bootstrapMethod="anti")

# use the epistemic bootstrap

list1Epistemic<-EpistemicBootstrap(list1$value,cutsNumber = 10)

# calculate the standard deviation using the obtained output

EpistemicEstimator(list1Epistemic,estimator="sd")