chimeas {POT} | R Documentation

## 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 chibar 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 ~ 1} 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 chibar is only useful for asymptotically independent variables. Indeed, for asymptotically dependent variable, we have lim_{u ~ 1}chibar(u) = 1. For asymptotically independent variables, lim_{u ~ 1}chibar(u) reflects the strength of the dependence between variables. For independent variables, chibar(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)

[Package POT version 1.1-7 Index]