# bootgpd: Parametric bootstrap for generalized Pareto models In texmex: Threshold exceedences and multivariate extremes

## Description

Parametric bootstrap for fitted generalized Pareto models with or without covariates

## Usage

 ```1 2 3``` ```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.

## 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.

## 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

## Author(s)

Harry Southworth

`gpd`, `bootmex`
 ```1 2 3 4 5``` ```mod <- gpd(log(ALT.M), data=liver, qu=.7, xi=~as.numeric(dose)) bmod <- bootgpd(mod) summary(bmod) par(mfrow=c(1,3)) plot(bmod) ```