f_PseudoBlocks {boodd}R Documentation

Compute the Value of the Function on a (Pseudo)-Regenerative Blocks.

Description

Function is an adaptation of GetPseudoBlocks to compute the value of any function on pseudo-regenerative blocks.

Usage

f_PseudoBlocks(x, s, eps_opt, delta_opt, p_XiXip1, func = sum)

Arguments

x

A vector or time series.

s

A real number specifying the center of the small set.

eps_opt

A numeric value for the size of the small set.

delta_opt

A numeric value for the lower bound in the minorization condition.

p_XiXip1

A numeric value representing the estimator of the transition density.

func

A function to apply to each block. Default is sum.

Details

This function computes the value of a specified function on pseudo-regenerative blocks of a time series. It uses parameters such as the central value (s), the size of the small set (eps_opt), and the lower bound in the minorization condition (delta_opt). Robustification is not proposed here due to the complexity of the pseudo-regenerative procedure.

Value

A matrix with two columns:

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

GetPseudoBlocks, regenboot, findBestEpsilon, GetBlocks, smallEnsemble.

Examples


n=1000 
coeff=0.75
X = arima.sim(n=n, list(ar = c(coeff)))
sm <- findBestEpsilon(X,s=0,plotIt=FALSE)
eps = sm$epsilon
delta = sm$delta
m = sm$s
f = sm$trans
result <- f_PseudoBlocks(X, 0, eps, delta, f, func = max)
print(result)


[Package boodd version 0.1 Index]