thetaRB {boodd}R Documentation

Compute the Extremal Index for Atomic Markov Chains Using Regenerative Blocks

Description

This function divides the input dataset into blocks for an atomic Markov chain and calculates the extremal index using quantile-based thresholds.

Usage

thetaRB(X, ato)

Arguments

X

A numeric vector representing the Markov chain.

ato

A numeric value; the atom of the Markov chain.

Details

The function uses GetBlocks to divide X into blocks according to the atom ato. High quantiles from X are generated and used as thresholds to compute statistics on each block, including sub-maximums and block indices. These statistics are then used to calculate the extremal index, a measure of extreme value clustering, across the blocks.

Value

A numeric vector representing the extremal index at various quantile thresholds.

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). Regeneration-based statistics for Harris recurrent Markov chains. Lecture notes in Statistics, vol. 187, pp. 1-54, Springer.

Bertail, P., Clémençon, S. and Tressou, J. (2009). Extreme values statistics for Markov chains via the (pseudo-) regenerative method. Extremes, 12, 327–360.

See Also

GetBlocks, regenboot.

Examples

X = genMM1(1000, 1, 2)
thetaB <- thetaRB(X, ato=0)
plot(thetaB)

[Package boodd version 0.1 Index]