bootmex(x, R = 100, nPass=3, trace=10)
"plot"(x, plots = "gpd", main = "", ...)
"print"(x, ...)mex. R=100. trace=10.margins in the original call to mex). The sample size and data dimension match that of the original data set. Then an empirical bootstrap sample is generated from the original data after its transformation to the Gumbel/Laplace scale. Again, sample size and structure match the original data set. The empirical bootstrap samples from each margin are then sorted, and then replaced by their corresponding values from the sorted Gumbel/Laplace samples. This procedure preserves the dependence structure of the empirical bootstrap sample while ensuring the marginal properties of the resulting semi-parametric bootstrap sample are those of the parametric Gumbel/Laplace distribution.The simulated, ordered Laplace/Gumbel sample is then transformed to the scale of the original data by using the Probability Integral Transform. Values beneath the original thresholds for fitting of the GPD tail models are transformed by using the empirical distribution functions and for values above these thresholds, the fitted GPDs are used. This completes the semi-parametric bootstrap from the data.
Parameter estimation is then carried out as follows: The parameters in the generalized Pareto distributions are estimated by using the bootrap data, these data are then transformed to the Laplace/Gumbel scale using the orginal threshold, their empirical distribution function and these estimated GPD 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. The function bootmex does whatever was done in the call to migpd or mex that generated the object with which it is being called.
Also note that sometimes (again, usually with small data sets) all of the simulated Laplace/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.
migpd, mexDependence ,
bootmex, predict.mex.
# Uncomment the following lines to run example - commented out to keep CRAN happy
#mymex <- mex(winter , mqu = .7, dqu = .7, which = "NO")
#myboot <- bootmex(mymex)
#myboot
#plot(myboot,plots="gpd")
#plot(myboot,plots="dependence")
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