mexRangeFit {texmex}

Estimate dependence parameters in a conditional multivariate extreme values model over a range of thresholds.

Description

Diagnostic tool to aid the choice of threshold to be used for the estimation of the dependence parameters in the conditional multivariate extreme values model of Heffernan and Tawn, 2004.

Usage

mexRangeFit(x, which, quantiles = seq(0.5, 0.9, length = 9),
start=c(.01, .01), R = 10, nPass=3, trace=10, margins = "laplace", constrain
= TRUE, v = 10, referenceMargin=NULL)

Arguments

x

An object of class mex or migpd.

which

The variable on which to condition.

quantiles

A numeric vector specifying the quantiles of the marginal distribution of the conditioning variable at which to fit the dependence model.

start

See documentation for this argument in mexDependence.

R

The number of bootstrap runs to perform at each threshold. Defaults to R=10.

nPass

Argument passed to function bootmex.

trace

Argument passed to function bootmex.

margins

Argument passed to function mexDependence.

constrain

Argument passed to function mexDependence.

v

Argument passed to function mexDependence.

referenceMargin

Optional set of reference marginal distributions to use for marginal transformation if the data's own marginal distribution is not appropriate (for instance if only data for which one variable is large is available, the marginal distributions of the other variables will not be represented by the available data). This object can be created from a combination of datasets and fitted GPDs using the function makeReferenceMarginalDistribution.

Details

Dependence model parameters are estimated using a range of threshold values. The sampling variability of these estimates is characterised using the bootstrap. Point estimates and bootstrap estimates are finally plotted over the range of thresholds. Choice of threshold should be made such that the point estimates at the chosen threshold and beyond are constant, up to sampling variation.

Value

NULL.

Author(s)

Harry Southworth, Janet E. Heffernan

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

mexDependence, bootmex

Examples

  w <- migpd(winter, mqu=.7)
  w
  par(mfrow=c(4,2))
  plot(mexRangeFit(w, which=1),main="Winter data, Heffernan and Tawn 2004",cex=0.5)