regenboot {boodd}R Documentation

Regenerative and Approximative Regenerative Block Bootstrap.

Description

Performs regenerative block bootstrap and approximately regenerative block bootstrap on a Markov chain, either in the atomic case or in the general Harris case.

Usage

regenboot(
  x,
  func,
  B,
  ...,
  atom,
  small = NULL,
  s = median(x),
  plotIt = FALSE,
  moon = length(x)
)

Arguments

x

A numeric vector representing a Markov process.

func

The function to apply to each sample.

B

A positive integer; the number of bootstrap replications.

...

Optional additional arguments for the func function.

atom

A numeric value or a string; an atom of the Markov chain in the atomic case.

small

An object of class smallEnsemble. It can be created optimally using the function findBestEpsilon.

s

A real number specifying the center of the small set. Default is the median of x.

plotIt

Logical. If TRUE then the function returns a plot of the time series with the approximative regenerative blocks. Does not plot anything in the atomic case. Default is FALSE.

moon

A positive integer. Default is length of x. moon should be smaller than the length of x, then it creates bootstrap samples of size moon.

Details

This function regenboot implements two different kinds of regenerative bootstrap:

One must specify either the atom argument or the small argument. In the first case, atom is the state used to split the Markov chain into blocks ending with the atom. In the second case, small is an object of class smallEnsemble representing the small ensemble. Such objects are typically obtained using the findBestEpsilon function but may also be constructed manually using the smallEnsemble function.

Value

returns an object of class boodd.

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. (2006a). Regenerative Block Bootstrap for Markov Chains. Bernoulli, 12, 689-712.

Bertail, P. and Clémençon, S. (2006b). Regeneration-based statistics for Harris recurrent Markov chains. Lecture notes in Statistics, vol. 187, pp. 1-54, Springer.

Radulović, D. (2004). Renewal type bootstrap for Markov chains. Test, 13, 147-192.

See Also

boots, blockboot, plot.boodd, confint.boodd, findBestEpsilon,smallEnsemble.

Examples


B <- 299
n <- 200

# Atomic Boostrap
acgt <- c("A","C","G","T")
probs <- c(.3,.1,.3,.3)
atom <- "C"
set.seed(1)
x <- sample(acgt,n,prob=probs,repl=TRUE)
propAtom <- function(x) {
  tbl <- as.vector(table(x))
  prop <- tbl[3]/length(x)
   return(prop)
}
boo <- regenboot(x,propAtom,B,atom=atom)
plot(boo)

# Approximate regenerative bootstrap with estimated small set
ar <- arima.sim(list(c(1,0,0),ar=0.6),n=500)
# Find the small ensemble with the largest number of regenerations
sm <- findBestEpsilon(ar,s=0,plotIt=TRUE)
# Approximate regenerative bootstrap of the mean
rboo <- regenboot(ar,mean,small=sm,B=999, plotIt=TRUE)
# Plot the corresponding bootstrap distribution
plot(rboo)
# Compute the bootstrap percentile confidence interval
confint(rboo)


[Package boodd version 0.1 Index]