ftrunc {boodd}R Documentation

Robust Estimators of the Mean Based on Regeneration Blocks.

Description

The function calculates various statistics (mean, median, truncated, and Winsorized mean) based on regeneration blocks obtained from the data. It also computes the mean block size. It relies on block-based calculations for robust statistics by eliminating either too large blocks or too large values of the mean on a given block.

Usage

ftrunc(x, atom_f, m = quantile(x, 0.05), M = quantile(x, 0.95), trunc)

Arguments

x

A vector or time series.

atom_f

A numeric value specifying an atom of the Markov chain.

m

A numeric value; the lower truncation threshold Default is the 5th percentile of x.

M

A numeric value; the upper truncation threshold Default is the 95th percentile of x.

trunc

A numeric value specifying the truncation threshold for computing the truncated and Winsorized means of the block length.

Details

This function uses blocks obtained from the input data x to compute several descriptive statistics, including the mean size of blocks, overall mean, median, and robust estimates like truncated and Winsorized means. The function internally uses GetBlocks to divide the input data into regenerative blocks when the process hits the atom atom_f.

The parameters m and M represent the lower and upper truncation thresholds, respectively. By default, these are set to the 5th and 95th percentiles of the input data, but they can be manually adjusted by the user to perform customized truncation.

The parameter trunc is used to eliminate blocks which lengths are greater than trunc.

Value

A numeric vector containing the following elements:

References

Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.

Bertail, P., Clémençon, S. and Tressou, J. (2015). Bootstrapping Robust Statistics for Markovian Data Applications to Regenerative R‐Statistics and L‐Statistics. Journal of Time Series Analysis, 36, 462–480.

See Also

GetBlocks, findBestEpsilon, GetPseudoBlocks, smallEnsemble, regenboot.

Examples

n=500 # the length of the process
lambda=0.6 # arrival rate
mu=0.8 # departure rat
X = genMM1(n,lambda,mu) # generate MM1 queue
atom = 0 # specify the atom
trunc = 30 # set truncation threshold
result = ftrunc(x=X, atom_f=atom, m=0, trunc = trunc) # apply function
print(result)


[Package boodd version 0.1 Index]