get.gam.fit() extracts a convenient list containing unique
covariate combinations and corresponding fitted values from an
object returned by gam().
gam.predict() computes a convenient list containing unique
covariate combinations and corresponding predicted values and
pointwise asymptotic confidence intervals (obtained from the estimated
standard errors obtained by predict(..., se.fit=TRUE)).
get.GPD.fit() extracts a convenient list containing (for each
of the GPD parameters) unique
covariate combinations, the fitted GPD parameter (vector),
bootstrapped pointwise two-sided 1-\(\alpha\) confidence
intervals, and a matrix of bootstrapped parameter values.
GPD.predict() computes a convenient list containing (for each
of the GPD parameters) unique
covariate combinations and corresponding predicted values.
risk.measure() computes the selected risk measure at a matrix
of values for \(\rho\), \(\xi\), \(\beta\).
get.gam.fit(x)
gam.predict(x, newdata=NULL, alpha=0.05, value=c("lambda", "rho"))
get.GPD.fit(x, alpha=0.05)
GPD.predict(x, xi.newdata=NULL, beta.newdata=NULL)risk.measure(x, alpha, u, method = c("VaR", "ES"))
For get.gam.fit() and gam.predict()
an object as returned by gam(); for
get.GPD.fit() and GPD.predict() an object as returned by
gamGPDboot(); for risk.measure() a matrix with
three columns containing an estimate \(\rho\) of the tail of
the loss distribution at the threshold u for a covariate
combination, the corresponding \(\xi\) and the
corresponding \(\beta\) (in this order).
object as required by
predict(). Typically a named data.frame
of type expand.grid(covar1=, covar2=) with at least the covariates
used for fitting with gam(); if more are provided,
predict() returns values which are equal uniformly
over all of these additional covariates. Each covariate which
appears when fitting with gam() can
have more values than were actually used in gam().
In this case predict() “interpolates” correctly with the
fitted model.
as newdata, just for the GPD
parameters \(\xi\) and \(\beta\).
for gam.predict(),
get.GPD.fit() the significance level
(typcially 0.05); for risk.measure() the confidence level
(typically close to 1).
threshold.
either "lambda" or "rho" depending on
whether \(\lambda\) or \(\rho\) is predicted.
character string indicating the kind of
risk measure (Value-at-Risk (VaR) or expected shortfall
(ES)).
get.gam.fit() returns a list with components
covar:(unique/minimalized) covariate combinations;
fit:corresponding fitted values of lambda or rho.
gam.predict() returns a list with components
covar:covariate combinations as provided by newdata;
predict:predicted lambda or rho;
CI.low:lower confidence interval (based on predicted values);
CI.up:upper confidence interval (based on predicted values).
get.GPD.fit() returns a list with components
xi:list with components
covar:(possibly empty) data.frame containing
the unique/minimal covariate combinations for the covariates used
for fitting \(\xi\);
fit:corresponding fitted \(\xi\);
CI.low:lower confidence interval (bootstrapped pointwise two-sides 1-\(\alpha\));
CI.up:upper confidence interval (bootstrapped pointwise two-sides 1-\(\alpha\));
boot:matrix containing the
corresponding bootstrapped \(\xi\)'s (or NULL if
none of the bootstrap repetitions worked).
beta:similar as for xi.
GPD.predict() returns a list with components
xi:list with components
covar:data.frame containing the
covariate combinations as provided by xi.newdata;
predict:predicted \(\xi\)'s;
beta:similar as for xi.
risk.measure() returns a vector of values of the selected risk measure.
Note that if gam() fails in gamGPDfit() or the
fitting or one of the bootstrap replications in gamGPDboot(),
then x contains (an) empty (sub)list(s). These empty lists will
be removed from the output of get.GPD.fit(). Hence, the
subcomponent xi$fit of the output of get.GPD.fit() can
contain less columns than the chosen number of bootstrap replications
for creating x (each bootstrap replication with failed
gam() calls is omitted). If there is any such failure,
get.GPD.fit() outputs a warning. These
failures typically happen for too small sample sizes.
Chavez-Demoulin, V., Embrechts, P., and Hofert, M., An extreme value approach for modeling Operational Risk losses depending on covariates.
# NOT RUN {
## see demo(game) for how to use these functions
# }
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