kgaps_imt_stat

Calculates the components required to calculate the value of the information
matrix test under the \(K\)-gaps model, using vector data input.
Called by <code>kgaps_imt</code>.

Performs frequentist inference for the extremal index of a
stationary time series. Two types of methodology are used. One type is
based on a model that relates the distribution of block maxima to the
marginal distribution of series and leads to the semiparametric maxima
estimators described in Northrop (2015) <doi:10.1007/s10687-015-0221-5> and
Berghaus and Bucher (2018) <doi:10.1214/17-AOS1621>. Sliding block maxima
are used to increase precision of estimation. A graphical block size
diagnostic is provided. The other type of methodology uses a model for the
distribution of threshold inter-exceedance times (Ferro and Segers (2003)
<doi:10.1111/1467-9868.00401>). Three versions of this type of approach are
provided: the iterated weight least squares approach of Suveges (2007)
<doi:10.1007/s10687-007-0034-2>, the K-gaps model of
Suveges and Davison (2010) <doi:10.1214/09-AOAS292> and a similar approach
of Holesovsky and Fusek (2020) <doi:10.1007/s10687-020-00374-3>
that we refer to as D-gaps. For the K-gaps and D-gaps models this 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 right-censored inter-exceedance times.
Graphical diagnostics for the threshold level and the respective tuning
parameters K and D are provided.

Paul Northrop

exdex

Estimation of the Extremal Index

Constantinos Christodoulides

kgaps_imt_stat function

<dl><dt>data</dt>
<dd>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 <code><a href="/link/na.omit?package=exdex&version=1.2.3" data-mini-rdoc="exdex::na.omit">na.omit</a></code>.</dd>
<dt>theta</dt>
<dd>A numeric scalar. An estimate of the extremal index
\(\theta\), produced by <code>kgaps</code>.</dd>
<dt>u</dt>
<dd>A numeric scalar. Extreme value threshold applied to data.</dd>
<dt>k</dt>
<dd>A numeric scalar. Run parameter \(K\), as defined in Suveges and
Davison (2010). Threshold inter-exceedances times that are not larger
than <code>k</code> 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
\(S = \max(T - K, 0)\).</dd>
<dt>inc_cens</dt>
<dd>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.</dd></dl>

Arguments

Statistics for the information matrix test — kgaps_imt_stat

<dl>

<dt>data</dt>
<dd>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 <code><a href='https://rdrr.io/r/stats/na.fail.html'>na.omit</a></code>.</dd>


<dt>theta</dt>
<dd>A numeric scalar. An estimate of the extremal index
\(\theta\), produced by <code>kgaps</code>.</dd>


<dt>u</dt>
<dd>A numeric scalar. Extreme value threshold applied to data.</dd>


<dt>k</dt>
<dd>A numeric scalar. Run parameter \(K\), as defined in Suveges and
Davison (2010). Threshold inter-exceedances times that are not larger
than <code>k</code> 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
\(S = \max(T - K, 0)\).</dd>


<dt>inc_cens</dt>
<dd>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.</dd>

</dl>

kgaps_imt_stat: Statistics for the information matrix test

Description

Usage

Value

Arguments

References