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.
kgaps_imt_stat(data, theta, u, k = 1, inc_cens = TRUE)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.
A numeric scalar. An estimate of the extremal index
\(\theta\), produced by kgaps.
A numeric scalar. Extreme value threshold applied to data.
A numeric scalar. Run parameter \(K\), as defined in Suveges and
Davison (2010). Threshold inter-exceedances times that are not larger
than k units 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
\(S = \max(T - K, 0)\).
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.
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 \(\theta\).
ldj the derivative of the log-likelihood with respect to \(\theta\) (the score)
Ij the observed information
Jj the square of the score
dj Jj - Ij
Ddj the derivative of Jj - Ij with respect
to \(\theta\)
n_kgaps the number of \(K\)-gaps that contribute to the log-likelihood.
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