QRM: game-aux – R documentation

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game-aux

Auxiliary Functions for Extracting/Computing Results Related to gamGPDfit()/gamGPDboot()

Description

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.

Usage

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"))

Arguments

`x`	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).
`newdata`	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.
`xi.newdata, beta.newdata`	as `newdata`, just for the GPD parameters xi and beta.
`alpha`	for `gam.predict()`, `get.GPD.fit()` the significance level (typcially 0.05); for `risk.measure()` the confidence level (typically close to 1).
`u`	threshold.
`value`	either `"lambda"` or `"rho"` depending on whether lambda or rho is predicted.
`method`	`character` string indicating the kind of risk measure (Value-at-Risk (`VaR`) or expected shortfall (`ES`)).

Details

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.

Value

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.

Author(s)

Marius Hofert

References

Chavez-Demoulin, V., Embrechts, P., and Hofert, M., An extreme value approach for modeling Operational Risk losses depending on covariates.

Examples

## see demo(game) for how to use these functions

QRM

Provides R-Language Code to Examine Quantitative Risk Management Concepts

v0.4-31

GPL (>= 2)

Authors

Bernhard Pfaff [aut, cre], Marius Hofert [ctb], Alexander McNeil [aut] (S-Plus original (QRMlib)), Scott Ulmann [trl] (First R port as package QRMlib)

Initial release

2020-02-15