texmex (version 1.3)

bootgpd: Parametric bootstrap for generalized Pareto models

Description

Parametric bootstrap for fitted generalized Pareto models with or without covariates

Usage

bootgpd(x, R = 100, trace = 10)
## S3 method for class 'bootgpd':
plot(x, col=4, border=FALSE, ...)

Arguments

x

An object of class 'gpd'

R

The number of bootstrap replicates to simulate. Defaults to R = 100.

trace

Report progress to the user every trace replicates. Defaults to trace = 10.

col

Colour of histogram bars

border

Whether or not to draw borders between histogram bars

...

Further arguments to plot method.

Value

• call
  The function call
• replicates
  The bootstrap parameter estimates
• summary.bootgpd: margins
  Summary of the marginal parameter estiamtes
• summary.bootgpd: covariance
  Covariance of the parameter estimates

Details

The design matrices for phi and xi are held fixed and random deviates from the fitted GPD corresponding to these design matrices are generated. Especially for small sample sizes, non-parameteric bootstrapping of GPD models can result in unreasonable distributions (such as bimodal) due to small numbers of observed extreme values having considerable influence on parameter estimates in a minority of samples. Therefore, only parametric bootstrapping is implemented here.

The print method returns the original point estimates, bootstrap means, bootstrap estimates of bias and standard deviation. The bootstrap median is also returned.

The summary method returns the same as the print method, but also the bootstrap estimate of the covariance of the parameters. When printed, the correlation (not covariance) is displayed. The covariance might be wanted so that it can be passed into gpd using method = "simulate". In some circumstances the numerical estimate of the Hessian of the parameters can be unstable, resulting in the Metropolis algorithm using a proposal distribution that is too narrow. This shows up as the acceptance rate of the algorithm being too high (above about 45%). Then, using a bootstrap estimate might be preferable.

The plot method displays histograms and kernel density estimates.

See Also

gpd, bootmex

Examples

mod <- gpd(log(ALT.M), data=liver, qu=.7, xi=~as.numeric(dose))
# Keep R low to keep CRAN happy. Use many more than this in any
# real application.
bmod <- bootgpd(mod, R=20)
summary(bmod)
par(mfrow=c(1,3))
plot(bmod)