kgaps_imt_stat: Statistics for the information matrix test

In exdex: Estimation of the Extremal Index

Statistics for the information matrix test

Description

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.

Usage

kgaps_imt_stat(data, theta, u, k = 1, inc_cens = TRUE)

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 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).
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.

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.

References

Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, Annals of Applied Statistics, 4(1), 203-221. \Sexpr[results=rd]{tools:::Rd_expr_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

exdex documentation built on Sept. 10, 2023, 5:06 p.m.