chimeas: Dependence Measures For Extreme Values Analysis

In POT: Generalized Pareto Distribution and Peaks Over Threshold

Dependence Measures For Extreme Values Analysis

Description

Provide two measures to assess for asymptotic dependence or independence

Usage

chimeas(data, u.range, n.u = 500, xlab, ylabs, ci = 0.95,  boot = FALSE,
n.boot = 250, block.size = 50, show.bound = TRUE, which = 1:2, ask =
nb.fig < length(which) && dev.interactive(), ..., col.ci = "grey",
col.bound = "blue", lty.ci = 1, lty.bound = 1)

Arguments

data	A matrix with 2 columns with the data.
u.range	Numeric vection of length 2 (may be missing): the range for the probabilities.
n.u	The number of probabilities to be considered
xlab, ylabs	The x-axis and ylabs labels. ylabs must be of length 2
ci	The probability level for the confidence intervals
boot	Logical. If TRUE, confidence intervals are computed by bootstraping contiguous blocks. This may be needed if there is dependence between observations. If FALSE (the default), confidence intervals are derived using the Delta method.
n.boot	The number of bootstrap replicates.
block.size	The size of the “contiguous” blocks. See details.
show.bound	Logical. If TRUE (the default), the theoretical bound for the two statistics are plotted.
which	Which plot should be plotted? 1 for the \chi 2 for the \overline{\chi} statistic and 1:2 for both of them.
ask	Logical. Should user be asked before each plot is computed?
...	Additional options to be passed to the plot function.
col.ci, col.bound	The color for the confidence intervals and theoretical bounds.
lty.ci, lty.bound	The line type for the confidence intervals and theoretical bounds.

Details

These two plots help us to understand the dependence relationship between the two data set. The sign of \chi(u) determines if the variables are positively or negatively correlated. Two variable are asymptotically independent if \lim_{u\rightarrow1} \chi(u) = 0. For the independent case, \chi(u) = 0 for all u in (0,1). For the perfect dependence case, \chi(u) = 1 for all u in (0,1). Note that for a bivariate extreme value model, \chi(u) = 2(1 - A(0.5)) for all u in (0,1).

The measure \overline{\chi} is only useful for asymptotically independent variables. Indeed, for asymptotically dependent variable, we have \lim_{u\rightarrow 1}\overline{\chi}(u) = 1. For asymptotically independent variables, \lim_{u\rightarrow 1}\overline{\chi}(u) reflects the strength of the dependence between variables. For independent variables, \overline{\chi}(u) = 0 for all u in (0,1).

If there is (short range) dependence between observations, users may need to use bootstrap confidence intervals. Bootstrap series are obtained by sampling contiguous blocks, of length l say, uniformly with replacement from the original observations. The block length l should be chosen to be much greater than the short-range dependence and much smaller than the total number of observations.

Value

A graphic window.

Author(s)

Mathieu Ribatet

References

Coles, S., Heffernan, J. and Tawn, J. (1999) Dependence measures for extreme value analyses. Extremes 2 339–365.

See Also

tailind.test, specdens, tsdep.plot

Examples

mc <- simmc(200, alpha = 0.9)
mc2 <- simmc(100, alpha = 0.2)
##An independent case
par(mfrow = c(1,2))
chimeas(cbind(mc[1:100], mc2))
##Asymptotic dependence
par(mfrow = c(1,2))
chimeas(cbind(mc[seq(1,200, by = 2)], mc[seq(2,200,by = 2)]))
##The same but with bootstrap ci
par(mfrow = c(1,2))
chimeas(cbind(mc[seq(1,200, by = 2)], mc[seq(2,200,by = 2)]), boot =
TRUE, n.boot=50)

POT documentation built on Oct. 17, 2024, 5:06 p.m.