smallEnsemble {boodd}R Documentation

Class smallEnsemble

Description

Creates an object of class smallEnsemble, typically used in regenerative bootstrap methods for Markov chains. This function allows manual specification of parameters for the small ensemble.

Usage

smallEnsemble(s, eps, delta, trans)

Arguments

s

A numeric value specifying the center of the small set.

eps

A positive numeric value; the radius of the small set.

delta

A positive numeric value; a lower bound for the transition density over the small set, controlling the Nummelin splitting trick.

trans

A vector representing the estimated transition density between X_i and X_{i+1}. This can be calculated using fastNadaraya.

Details

The smallEnsemble object is used in regenerative bootstrap methods, particularly in the context of Markov chains. It defines a small set, characterized by a central point s, a radius eps, and a lower bound delta.

This function is useful for users who wish to manually specify the parameters of the small set, as opposed to using automated methods like findBestEpsilon, which returns a smallEnsemble object.

Value

Returns an object of class smallEnsemble, containing the specified parameters for the small set and the transition density.

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.

See Also

regenboot, findBestEpsilon, fastNadaraya.

Examples

# Example of creating a smallEnsemble object
# Assuming a Markov chain data
data <- rnorm(100)
s <- median(data)   # Middle point of the small set
eps <- 0.5          # Width of the small set
delta <- 0.1        # Parameter of the small set
# Define a simple transition kernel function
trans <- fastNadaraya(data, 1/10)
# Create the smallEnsemble object
small_ensemble <- smallEnsemble(s, eps, delta, trans)


[Package boodd version 0.1 Index]