Calculates the components required to calculate the value of the information
matrix test under the \(K\)-gaps model, using vector data input.
Called by kgaps_imt.
Arguments
- data
A numeric vector of raw data. Missing values are allowed, but they should not appear between non-missing values, that is, they only be located at the start and end of the vector. Missing values are omitted using
na.omit.- theta
A numeric scalar. An estimate of the extremal index \(\theta\), produced by
kgaps.- u
A numeric scalar. Extreme value threshold applied to data.
- k
A numeric scalar. Run parameter \(K\), as defined in Suveges and Davison (2010). Threshold inter-exceedances times that are not larger than
kunits are assigned to the same cluster, resulting in a \(K\)-gap equal to zero. Specifically, the \(K\)-gap \(S\) corresponding to an inter-exceedance time of \(T\) is given by \(S = \max(T - K, 0)\).- inc_cens
A logical scalar indicating whether or not to include contributions from censored inter-exceedance times relating to the first and last observation. See Attalides (2015) for details.
Value
A list relating the quantities given on pages 18-19 of
Suveges and Davison (2010). All but the last component are vectors giving
the contribution to the quantity from each \(K\)-gap, evaluated at the
input value theta of \(\theta\).
ldjthe derivative of the log-likelihood with respect to \(\theta\) (the score)
Ijthe observed information
Jjthe square of the score
djJj-IjDdjthe derivative of
Jj-Ijwith respect to \(\theta\)n_kgapsthe number of \(K\)-gaps that contribute to the log-likelihood.
References
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
Attalides, N. (2015) Threshold-based extreme value modelling, PhD thesis, University College London. https://discovery.ucl.ac.uk/1471121/1/Nicolas_Attalides_Thesis.pdf