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

threshvalue of threshold returned by the procedure, NA if the hypothesis is rejected at all thresholds
cthreshsorted vector of candidate thresholds
cindexindex of selected threshold among cthresh or NA if none returned
pvalbootstrap p-values, with NA if lazy and the p-value exceeds level at lower thresholds
shapeshape parameter estimates
nexcnumber of exceedances of each threshold cthresh
methodestimation 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.