Methods for objects of class "flite" returned from
flite.
# S3 method for flite
plot(
x,
which = c("all", "pu", "gp", "xi", "theta"),
adj_type = c("vertical", "none", "cholesky", "spectral"),
...
)
# S3 method for flite
coef(object, ...)
# S3 method for flite
vcov(object, adjust = TRUE, ...)
# S3 method for flite
nobs(object, ...)
# S3 method for flite
logLik(object, ...)
# S3 method for flite
summary(object, adjust = TRUE, digits = max(3, getOption("digits") - 3L), ...)
# S3 method for summary.flite
print(x, ...)
# S3 method for flite
confint(
object,
parm = "all",
level = 0.95,
adj_type = c("vertical", "none", "cholesky", "spectral"),
profile = TRUE,
...
)An object inheriting from class "flite", a result of a
call to flite.
A character scalar indicating which plot(s) to produce.
If which = "all" then all 4 plots described in Details
are produced. Otherwise, only one of these plots is produced, with the
possible names of the arguments being in the order that the plots are
described in Details.
A character scalar passed to
conf_intervals and
conf_region as the argument type to select
the type of adjustment applied to the independence log-likelihood. Of the
3 adjustments, "vertical" is preferred because it preserves
constraints on the parameters, whereas the "cholesky" and
"spectral" adjustment do not. In the generalised Pareto case the
constraint that
\(\xi\) > -\(\sigma\)u /
\(x\)(n)
where \(x\)(n)
is the largest excesses of the threshold \(u\), is preserved.
For plot.flite: arguments passed to
plot, such as graphical parameters.
For print.summary.flite: additional arguments passed to
print.default.
For confint.flite: additional arguments passed to
conf_intervals.
Otherwise ... is unused.
An object of class "flite", returned by
flite.
A logical scalar. If adjust = TRUE then the elements
of the variance-covariance matrix corresponding to
(\(p\)u,
\(\sigma\)u, \(\xi\)),
are estimated using a sandwich estimator. See flite.
Otherwise, this matrix is the inverse of the observed information matrix.
An integer. Passed to signif to
round the values in the summary.
A character vector specifying the parameters for which
confidence intervals are required. The default, which = "all",
produces confidence intervals for all the parameters, that is,
\(p\)u,
\(\sigma\)u,
\(\xi\) and \(\theta\). If which = "gp" then intervals are
produced only for
\(\sigma\)u and
\(\xi\). Otherwise, parm must be a subset of
c("pu", "sigmau", "xi", "theta").
The confidence level required. A numeric scalar in (0, 1).
A logical scalar. If TRUE then confidence intervals
based on an (adjusted) profile loglikelihood are returned. If
FALSE then intervals based on approximate large sample normal
theory, which are symmetric about the MLE, are returned.
plot.flite: No return value, only the plot is produced.
coef.flite: a numeric vector of length 4 with names
c("p[u]", "sigma[u]", "xi", "theta"). The MLEs of the parameters
\(p\)u,
\(\sigma\)u,
\(\xi\) and \(\theta\).
vcov.flite: a \(4 \times 4\) matrix with row and
column names c("p[u]", "sigma[u]", "xi", "theta"). The estimated
variance-covariance matrix for the model parameters. If
adjust = TRUE then the elements corresponding to
\(p\)u,
\(\sigma\)u, and \(\xi\) are adjusted for cluster dependence using a sandwich estimator; otherwise they are not adjusted.
nobs.flite: a numeric vector of length 3 with names
c("p[u]", "gp", "theta"). The respective number of observations
used to estimate \(p\)u,
(\(\sigma\)u,
\(\xi\)) and \(\theta\).
logLik.flite: an object of class "logLik": a numeric scalar
with value equal to the maximised log-likelihood. This is the sum of
contributions from three fitted models, from a Bernoulli model for
occurrences of threshold exceedances, a generalised Pareto model for
threshold excesses and a \(K\)-gaps model for the extremal index.
The returned object also has attributes nobs, the numbers of
observations used in each of these model fits, and "df" (degrees
of freedom), which is equal to the number of total number of parameters
estimated (4).
summary.flite: an object containing the original function call and
a matrix of estimates and estimated standard errors with row names
c("p[u]", "sigma[u]", "xi", "theta"). The object is printed by
print.summary.flite.
print.summary.flite: the argument x is returned, invisibly.
confint.flite: a numeric matrix with 2 columns giving the lower and
upper confidence limits for each parameter. These columns are labelled
as (1-level)/2 and 1-(1-level)/2, expressed as a
percentage, by default 2.5% and 97.5%. The row names
are the names of the parameters supplied in parm.
For plot.flite, if which = "all" then 4 plots are
produced.
Top left: (adjusted) log-likelihood for the threshold exceedence probability \(p\)u, with a horizontal line indicating a 95% confidence interval for \(p\)u.
Top right: contour plot of the (adjusted) log-likelihood for the GP parameters (\(\sigma\)u, \(\xi\)), showing (25, 50, 75, 90, 95)% confidence regions. The linear constraint \(\xi\) > -\(\sigma\)u / \(x\) (n) is drawn on the plot.
Bottom left: (adjusted) log-likelihood for \(\xi\), with a horizontal line indicating a 95% confidence interval for \(\xi\).
Bottom right: log-likelihood for the extremal index \(\theta\), with a horizontal line indicating a 95% confidence interval for \(\theta\).
flite to perform frequentist threshold-based
inference for time series extremes.