The extremal index \(\theta\) is a measure of the degree of local dependence in the extremes of a stationary process. The exdex package performs frequentist inference about \(\theta\) using the methodologies proposed in Northrop (2015), Berghaus and Bucher (2018), Suveges (2007), Suveges and Davison (2010) and Holesovsky and Fusek (2020).
Functions to implement four estimators of the extremal index are provided, namely
spm: semiparametric maxima estimator, using block
maxima: (Northrop, 2015; Berghaus and Bucher, 2018)
kgaps: \(K\)-gaps estimator, using threshold
inter-exceedance times (Suveges and Davison, 2010)
dgaps: \(D\)-gaps estimator, using threshold
inter-exceedance times (Holesovsky and Fusek, 2020))
iwls: iterated weighted least squares estimator,
using threshold inter-exceedance times: (Suveges, 2007)
The functions choose_b, choose_uk and
choose_ud provide graphical diagnostics for choosing the
respective tuning parameters of the semiparametric maxima, \(K\)-gaps and
\(D\)-gaps estimators.
For the \(K\)-gaps and \(D\)-gaps models the `exdex` package allows missing values in the data, can accommodate independent subsets of data, such as monthly or seasonal time series from different years, and can incorporate information from censored inter-exceedance times.
See vignette("exdex-vignette", package = "exdex") for an
overview of the package.
Berghaus, B., Bucher, A. (2018) Weak convergence of a pseudo maximum likelihood estimator for the extremal index. Ann. Statist. 46(5), 2307-2335. doi:10.1214/17-AOS1621
Holesovsky, J. and Fusek, M. Estimation of the extremal index using censored distributions. Extremes 23, 197-213 (2020). doi:10.1007/s10687-020-00374-3
Northrop, P. J. (2015) An efficient semiparametric maxima estimator of the extremal index. Extremes 18(4), 585-603. doi:10.1007/s10687-015-0221-5
Suveges, M. (2007) Likelihood estimation of the extremal index. Extremes, 10, 41-55. doi:10.1007/s10687-007-0034-2
Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, Annals of Applied Statistics, 4(1), 203-221. doi:10.1214/09-AOAS292