Threshold selection via coefficient of variation

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

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

Value

a list with elements

thresh0: value of threshold returned by the procedure, NA if the hypothesis is rejected at all thresholds
thresh: sorted vector of candidate thresholds
cindex: index of selected threshold among thresh 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 thresh
method: estimation method for the shape parameter

References

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