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