findBestEpsilon {boodd}R Documentation

Optimal Size of Small Sets

Description

Determines the optimal radius \epsilon of small sets, which maximizes the expected number of regeneration blocks. Useful for identifying the parameters for splitting a Markov chain into almost independent blocks.

Usage

findBestEpsilon(x, s = median(x), plotIt = FALSE)

Arguments

x

A numeric vector representing a Markov chain.

s

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

plotIt

Logical. If TRUE plots the estimated expected number of regenerations as a function of the radius \epsilon.

Details

The findBestEpsilon calculates the optimal radius \epsilon and the corresponding lower bound \delta of the transition density for choosing the optimal small set of a Markov chain given the center s of a small set. It uses the fastNadaraya function to estimate the transition density p_n(X_i,X_{i+1}) taken at points (X_i,X_{i+1}).

Value

Returns an object of class smallEnsemble, which is a list containing:

References

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

Bertail, P. and Clémençon, S. (2006). Regenerative block bootstrap for Markov chains. Bernoulli, 12, 689-712.

See Also

regenboot, fastNadaraya, naradamar, GetBlocks, GetPseudoBlocks, smallEnsemble.

Examples


n=200 # the length of the process
# Generating the AR(1) process
sigma=1
coeff=0.75
X=arima.sim(n=n,list(ar=coeff, sd=sigma))
# Find the small ensemble with the largest number of regeneration
sm <- findBestEpsilon(X,s=0,plotIt=FALSE)


[Package boodd version 0.1 Index]