threshrange.plot: Threshold Selection Through Fitting Models to a Range of...

In extRemes: Extreme Value Analysis

Threshold Selection Through Fitting Models to a Range of Thresholds

Description

Find an appropriate threshold for GP or PP models by fitting them to a sequence of thresholds in order to find the lowest threshold that yields roughly the same parameter estiamtes as any higher threshold.

Usage

threshrange.plot(x, r, type = c("GP", "PP", "Exponential"), nint = 10, alpha = 0.05,
    na.action = na.fail, set.panels = TRUE, verbose = FALSE, ...)

Arguments

x	numeric vector of data.
r	numeric vector of length two giving the range of thresholds.
type	character string stating which model to fit.
nint	number of thresholds to use.
alpha	number between zero and one stating which 1 - alpha confidence level to use for the confidence limits.
na.action	function to be called to handle missing values.
set.panels	logical; should the function set the panels on the device (TRUE) or not (FALSE).
verbose	logical; should progress information be printed to the screen?
...	optional arguments to fevd.

Details

Several GP or PP (or exponential) models are fit to x according to a range of nint thresholds given by r. The estimated parameters are plotted against these thresholds along with their associated (1 - alpha) * 100 percent CIs.

Choice of threshold is a compromise between low variance (lower thresholds yield more data with which to fit the models) and bias (higher thresholds yield estimates that are less biased because model assumptions require very high thresholds, and it can happen that lower data values may be more abundant causing the model to be biased toward the wrong values) in the parameter estimates. An appropriate threshold should yield the same parameter estimates (within uncertainty) as would be fit for any model fit to higher thresholds. Therefore, the idea is to find the lowest possible threshold whereby a higher threshold would give the same results within uncertainty bounds.

See Coles (2001) sec. 4.3.4 and 4.4 for more information.

Note that the default uses maximum likelihood estimation. While it is possible to use other methods, it is not recommended because of efficiency problems.

Value

A matrix of parameter values and CI bounds for each threshold value is returned invisibly. A plot is created.

Author(s)

Eric Gilleland

References

Coles, S. (2001). An introduction to statistical modeling of extreme values, London, United Kingdom: Springer-Verlag, 208 pp.

See Also

fevd, mrlplot

Examples

data(Fort)
threshrange.plot(Fort$Prec, r = c(1, 2.25), nint=5)

## Not run: 
threshrange.plot(Fort$Prec, r=c(0.01,1), nint=30, verbose=TRUE)

threshrange.plot(Fort$Prec, r=c(0.2,0.8), type="PP", nint=15,
    verbose=TRUE)

threshrange.plot(Fort$Prec, r=c(0.2,0.8), type="PP", nint=15,
    optim.args=list(method="Nelder-Mead"), verbose=TRUE)


## End(Not run)

extRemes documentation built on May 29, 2024, 5:27 a.m.