mex(data, which, mth, mqu, dqu, margins = "laplace", constrain = TRUE, v = 10, penalty = "gaussian", maxit = 10000, trace = 0, verbose = FALSE, priorParameters = NULL)
"plot"(x, quantiles = seq(0.1, by = 0.2, len = 5), col = "grey", ...)
"predict"(object, which, pqu=0.99, nsim=1000, trace=10, ...)
"summary"(object, mth, probs=c(0.05, 0.5, 0.95), ...)
"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
equal to the number of columns in data. In summary.predict.mex, the thresholds over which to simulate
data from the fitted multivariate model. If not supplied, it is
taken to be the thresholds that were used to fit the dependence model on the
scale of the original data.
mth, you can
specify the quantile (a probability) above which to fit generalized Pareto
distributions. If this is a vector of length 1, the same quantile
will be used for each variable. Otherwise, it should be a vector
whose length is equal to the number of columns in data.dqu=0.7 will result in the
data with the highest 30% of values of the conditioning
variable being used to estimate the dependence parameters.
The same threshold will be used for each dependent variable.
If not supplied then the default is to set dqu=mqu[which]
the quantile corresponding to the threshold used to fit the
marginal model to the tail of the conditioning variable.
Note that there is no requirement for the quantiles used
for marginal fitting (mqu) and dependence fitting
(dqu) to be the same, or for them to be ordered in
any way.mexDependence.mexDependence.mexDependence.evm 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 should be a vector of length 2 corresponding
to the location of the Gaussian distribution; the second a 2x2 matrix
corresponding to the covariance matrix of the distribution.
The names should match the names of the columns of data.
If not provided, the default priors are independent normal, centred at zero, with
variance 10000 for phi=log(sigma) and 0.25 for xi. See the details section.plot method for objects of class mex, the colour for
points on scatterplots of residuals and original data respectively.
In plot method for objects of class predict.mex, the colours
of points for observed and simulated data respectively.mex 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 "predict.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
plot(p)
Run the code above in your browser using DataLab