texmex (version 1.1)

bootmex: Bootstrap a conditional multivariate extreme values model

Description

Bootstrap a conditional multivariate extreme values model following the method of Heffernan and Tawn, 2004. I'm grateful to Jan Heffernan for advice.

Usage

bootmex(x, which, R = 100, dth, dqu, nPass=3, trace=10)
## S3 method for class 'bootmex':
plot(x, plots = "gpd", main = "", ...)
## S3 method for class 'bootmex':
print(x, ...)
## S3 method for class 'bootmex':
show(x, ...)

Arguments

x

An object of class 'migpd' as returned by function migpd.

which

The name of the variable on which the conditioning is done. This should be the name of one of the columns in the data set that was passed to migpd.

R

The number of bootstrap runs to perform. Defaults to R=100.

dth

The threshold on the Gumbel scale to apply to the specified conditioning variable. Only one of dth or dqu should be provided. If x has class mex, the value is read from the object and need not

dqu

The quantile to threshold to the specified conditioning variable at. Only one of dth or dqu should be provided. If x has class mex, the value is read from the object and need not be pr

nPass

An integer. Sometimes, particularly with small samples, the estimation process fails with some bootstrap samples. The function has a look to see which runs fail and takes additional bootstrap samples in an attempt to get

trace

How often the inform the user of progress. Defaults to trace=10.

plots

Whether to do diagnostic plots of gpd parameter estimates or dependence parameter estimates. Defaults to "gpd".

main

Title for plots.

...

Further arguments to be passed to methods.

Value

• An object of class 'bootmex'. Print and plot functions are available.

Details

Details of the bootstrap method are given by Heffernan and Tawn (2004). Firstly, Gumbel data are simulated independently. A bootstrap sample of the Gumbel-transformed original data is then taken and the simulated Gumbel variables are sorted to match the sort order of this bootstrap sample. This procedure ensures the simulated data has the same dependence structure as the bootstrap sample. The simulated, ordered Gumbel data are then transformed to the scale of the original data. Values beneath the original threshold are passed through the empirical distribution function and values above that threshold are passed through the appropriate distribution function of the estimated generalized Pareto distribution. The parameters in the generalized Pareto distributions are then estimated, the data are transformed to the Gumbel scale using the orginal threshold, the empirical distribution function and these estimated parameters. The variables in the dependence structure of these variables are then estimated. Note that maximum likelihood estimation will often fail for small samples when the generalized Pareto distribution is being fit. Therefore it will often be useful to use penalized likelihood estimation. bootmex does whatever was done in the call to migpd. Also note that sometimes (again, usually with small data sets) all of the simulated Gumbel random numbers will be beneath the threshold for the conditioning variable. Such samples are abandoned by bootmex and a new sample is generated. This probably introduces some bias into the resulting bootstrap distributions. The plot method produces histograms of bootstrap gpd parameters (the default) or scatterplots of dependence parameters with the point estimates for the original data shown. By design, there is no coef method. The bootstrapping is done to account for uncertainty. It is not obvious that adjusting the parameters for the mean bias is the correct thing to do.

References

J. E. Heffernan and J. A. Tawn, A conditional approach for multivariate extreme values, Journal of the Royal Statistical society B, 66, 497 -- 546, 2004

See Also

migpd , link{mexDependence}, bootmex, predict.mex.

Examples

# Uncomment the following lines to run example - commented out to keep CRAN robots happy
#mygpd <- migpd(winter , mqu = .7)
#myboot <- bootmex(mygpd, which = "NO", dqu=.7)
#myboot
#plot(myboot,plots="gpd")
#plot(myboot,plots="dependence")