texmex (version 1.0)

mexDependence: Estimate the dependence parameters in a conditional multivariate extreme values model

Description

Estimate the dependence parameters in a conditional multivariate extreme values model using the approach of Heffernan and Tawn, 2004. Many thanks to Janet Heffernan for answering lots of questions.

Usage

mexDependence(x, which, dth, dqu)
## S3 method for class 'mexDependence':
print(x, ...)
## S3 method for class 'mexDependence':
show(x, ...)
## S3 method for class 'mexDependence':
plot(x, quantiles=seq(0.1, by=0.2, len=5), col="grey", ...)

Arguments

x

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

which

The name of the variable on which to condition. This is the name of a column of the data that was passed into. migpd

dth

A single number specifying a threshold on the transformed scale; i.e. the threshold to use when estimating the dependence structure. The model will be conditional on the which variable being over this value. Only on

dqu

A single number specifying a quantile on the transformed scale; i.e. the threshold to use when estimating the dependence structure. The model will be conditional on the which variable being over this quantile. Only

quantiles

A vector of quantiles taking values between 0 and 1 specifying the quantiles of the conditional distributions which will be plotted.

col

The color for points on scatterplots of residuals and original data.

...

Further arguments to be passed to methods.

Value

• An object of class mexDependence. There are print and plot functions available.

Details

The parameters a, b, c and d in the dependence structure described by Heffernan and Tawn (2004) are estimated. Estimation takes place in two steps: first, a and b are estimated; then, if a=0 and b is negative, parameters c and d are estimated. Otherwise c and d will be fixed at zero. The plot method produces diagnostic plots for the fitted dependence model described by Heffernan and Tawn, 2004. 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. Any trend in the location of these variables with the conditioning variable indicates a violation of the model assumption that the residuals Z are indpenendent of the conditioning variable. The absolute value of Z-mean(Z) is also plotted, again with the lowess curve showing the local mean of these points. These plots are intended to highlight any trend between the variability of the residuals Z and the conditioning variable. The final plots show the fitted quantiles (specified by quantiles) of the conditional distribution of each 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.

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, bootmex, predict.mex

Examples

data(winter)
mygpd <- migpd(winter , mqu=.7, penalty="none")
mexDependence(mygpd , which = "NO", dqu=.7)