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Threshold selection via coefficient of variation

Source: R/coefvariation.R
thselect.cv.Rd

This function computes the empirical coefficient of variation and computes a weighted statistic comparing the squared distance with the theoretical coefficient variation corresponding to a specific shape parameter (estimated from the data using a moment estimator as the value minimizing the test statistic, or using maximum likelihood). The procedure stops if there are no more than 10 exceedances above the highest threshold.

Usage

thselect.cv(
  xdat,
  thresh,
  method = c("mle", "wcv", "cv"),
  nsim = 999L,
  nthresh = 10L,
  level = 0.05,
  lazy = FALSE,
  plot = FALSE
)

Arguments

xdat

[vector] vector of observations

thresh

[vector] vector of threshold. If missing, set to \(p^k\) for \(k=0\) to \(k=\)nthresh

method

[string], either moment estimator for the (weighted) coefficient of variation (wcv and cv) or maximum likelihood (mle)

nsim

[integer] number of bootstrap replications

nthresh

[integer] number of thresholds, if thresh is not supplied by the user

level

[numeric] probability level for sequential testing procedure

lazy

[logical] compute the bootstrap p-value until the test stops rejecting at level level? Default to FALSE

plot

[logical] if TRUE, returns a plot of the p-value path

Value

a list with elements

  • thresh: value of threshold returned by the procedure, NA if the hypothesis is rejected at all thresholds

  • thresh0: sorted vector of candidate thresholds

  • cindex: index of selected threshold among thresh0 or NA if none returned

  • pval: bootstrap p-values, with NA if lazy and the p-value exceeds level at lower thresholds

  • shape: shape parameter estimates

  • nexc: number of exceedances of each threshold thresh0

  • method: estimation method for the shape parameter

Note

The authors suggest transformation of $$Y = -1/(X + c) + 1/c,$$ where \(X\) are exceedances and \(c=\sigma/\xi\) is the ratio of estimated scale and shape parameters. For heavy-tailed distributions with \(\xi > 0.25\), this may be preferable, but must be conducted outside of the function.

References

del Castillo, J. and M. Padilla (2016). Modelling extreme values by the residual coefficient of variation, SORT, 40(2), pp. 303–320.

Examples

thselect.cv(
 xdat = rgp(1000),
 thresh = qgp(seq(0,0.9, by = 0.1)),
 nsim = 99,
 lazy = TRUE,
 plot = TRUE)