Performs an information matrix test (IMT) to diagnose misspecification of the \(D\)-gaps model of Holesovsky and Fusek (2020).
dgaps_imt(data, u, D = 1, inc_cens = TRUE)A numeric vector or numeric matrix of raw data. If data
is a matrix then the log-likelihood is constructed as the sum of
(independent) contributions from different columns. A common situation is
where each column relates to a different year.
If data contains missing values then split_by_NAs is
used to divide the data into sequences of non-missing values.
Numeric vectors. u is a vector of extreme value
thresholds applied to data. D is a vector of values of the
left-censoring parameter \(D\), as defined in Holesovsky and Fusek
(2020). See dgaps.
Any values in u that are greater than all the observations in
data will be removed without a warning being given.
A logical scalar indicating whether or not to include
contributions from right-censored inter-exceedance times, relating to the
first and last observations. See dgaps.
An object (a list) of class c("dgaps_imt", "exdex")
containing
A length(u) by length(D) numeric matrix.
Column i contains, for \(D\) = D[i], the values of the
information matrix test statistic for the set of thresholds in
u. The column names are the values in D.
The row names are the approximate empirical percentage quantile levels
of the thresholds in u.
A length(u) by length(D) numeric matrix
containing the corresponding \(p\)-values for the test.
A length(u) by length(D) numeric matrix
containing the corresponding estimates of \(\theta\).
The input u and D.
The general approach follows Suveges and Davison (2010).
The \(D\)-gaps IMT is performed a over grid of all
combinations of threshold and \(D\) in the vectors u
and D. If the estimate of \(\theta\) is 0 then the
IMT statistic, and its associated \(p\)-value is NA.
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
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
dgaps for maximum likelihood estimation of the
extremal index \(\theta\) using the \(D\)-gaps model.
### Newlyn sea surges
u <- quantile(newlyn, probs = seq(0.1, 0.9, by = 0.1))
imt <- dgaps_imt(newlyn, u = u, D = 1:5)
### S&P 500 index
u <- quantile(sp500, probs = seq(0.1, 0.9, by = 0.1))
imt <- dgaps_imt(sp500, u = u, D = 1:5)
### Cheeseboro wind gusts (a matrix containing some NAs)
probs <- c(seq(0.5, 0.98, by = 0.025), 0.99)
u <- quantile(cheeseboro, probs = probs, na.rm = TRUE)
imt <- dgaps_imt(cheeseboro, u = u, D = 1:5)
### Uccle July temperatures
probs <- c(seq(0.7, 0.98, by = 0.025), 0.99)
u <- quantile(uccle720m, probs = probs, na.rm = TRUE)
imt <- dgaps_imt(uccle720m, u = u, D = 1:5)