mex(data, which, mth, mqu, dqu, margins = "laplace", constrain = TRUE, v = 10,
penalty = "gaussian", maxit = 10000, trace = 0, verbose = FALSE, priorParameters = NULL)## S3 method for class 'mex':
plot(x, quantiles = seq(0.1, by = 0.2, len = 5), col = "grey", ...)
## S3 method for class 'mex':
predict(object, which, pqu=0.99, nsim=1000, trace=10, ...)
## S3 method for class 'predict.mex':
summary(object, mth, probs=c(0.05, 0.5, 0.95), ...)
## S3 method for class 'predict.mex':
plot(x, pch=c(1, 3), col=c(2, 8), cex=c(1, 1), ask=TRUE, ...)
mex, the threshold above which to fit generalized Pareto distributions.
If this is a vector of length 1, the same threshold will be used for
each variable. Otherwise, it should be a vector whose length is
dqu=0.7 will result in the data with the highest 30 threshold will bemexDependence.mexDependence.mexDependence.gpd for more information.maxit = 10000.optim. Whether or not to inform the user of the progress of the
optimizer. Defaults to 0, indicating no trace.verbose = FALSE.penalty = 'gaussian'.
It is a named list, each element of which contains two
components: the first component splot method for objects of class mex, the color for points on scatterplots of residuals and original data respectively.
In plot method for objects of class predict.mex, the colours of poimex as returned by function mex.predict method. The quantile of the conditioning
variable above which it will be simulated for importance sampling based prediction. Defaults to pqu = .99.predict method. The number of simulated observations
to be generated for prediction.summary method for objects of class predict.mex: the quantiles of the conditional
distribution(s) to calculate. Defaults to 5%, 50% and 95%.col, each of which should be of length 2.ask = TRUE.mex returns an list of class mex containing the following three items:migpd.mexDependence.plot, summary, coef and predict methods for this class.A call to predict.mex does the importance sampling for prediction, and returns a list of class "predict.mex" for which there are print and plot methods available. The summary method for this class of object is intended to be used following a call to the predict method, to estimate quantiles or probabilities of threshold excesses for the fitted conditional distributions given the conditioning variable above the threshold for prediction. See examples below.
There are print, summary and
plot methods available for the class 'predict.mex'.
mex works as follows. First, Generalized Pareto distributions (GPD) are fitted to the upper tails of each of the marginal distributions of the data: the GPD parameters are estimated for
each column of the data in turn, independently of all other columns.
Then, the conditional multivariate approach of Heffernan and Tawn is
used to model the dependence between variables. The returned object is of class 'mex'.
This function is a wrapper for calls to migpd and mexDependence, which estimate parameters of the marginal and dependence components of the Heffernan and Tawn model respectively. See documentation of these functions for details of modelling issues including the use of penalties / priors, threshold choice and checking for convergence of parameter estimates. The plot method produces diagnostic plots for the fitted dependence model described by Heffernan and Tawn, 2004. The plots are best viewed by using the plotting area split by par(mfcol=c(.,.)) rather than mfrow, see examples below. Three diagnostic plots are produced for each dependent variable:
1) Scatterplots of the residuals Z from the fitted model of Heffernan and Tawn (2004) are
plotted against the quantile of the conditioning variable, with a lowess curve showing the local
mean of these points. 2) The absolute value of Z-mean(Z) is also plotted, again with the lowess curve showing
the local mean of these points. Any trend in the location or scatter of these variables with the conditioning variable
indicates a violation of the model assumption that the residuals Z are indepenendent of the conditioning
variable. This can be indicative of the dependence threshold used being too low. 3) The final plots show the original data (on the original scale) and the fitted quantiles (specified by quantiles) of the conditional distribution
of each dependent variable given the conditioning variable. A model that fits well will have good agreement between the
distribution of the raw data (shown by the scatter plot) and the fitted quantiles. Note that the raw data are a sample from the joint distribution, whereas the quantiles are those of the estimated conditional distribution given the value of the conditioning variable, and while these two distributions should move into the same part of the sample space as the conditioning variable becomes more extreme, they are not the same thing!
The predict method for mex works as follows. The returned object
has class 'predict.mex'. Simulated values of the dependent variables are created,
given that the conditioning variable is above its 100pqu quantile.
If predict.mex is passed an object object of class "mex"
then the simulated values are based only on the point estimate of the dependence
model parameters, and the original data. If predict.mex is passed an object
object of class "bootmex" then the returned value additionally
contains simulated replicate data sets corresponding to the bootstrap model parameter
estimates. In both cases, the simulated values based on the original data
and point estimates appear in component object$data$simulated. The
simulated data from the bootstrap estimates appear in object$replicates.
The plot method for class "oredict.mex" displays both the original
data and the simulated data generated above the threshold for prediction; it
shows the threshold for prediction (vertical line) and also the curve joining equal quantiles
of the marginal distributions -- this is for reference: variables that
are perfectly dependent will lie exactly on this curve.
migpd, mexDependence, bootmexw <- mex(winter, mqu=.7)
w
par(mfcol=c(3, 2))
plot(w)
par(mfcol=c(2,2))
p <- predict(w)
summary(p)
summary(p,probs=c(0.01,0.2,0.5,0.8,0.99))
summary(p,probs=0.5,mth=c(40,50,150,25,50))
p
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