Parameter stability plots for peaks-over-threshold

This function computes the maximum likelihood estimate at each provided threshold and plots the estimates (pointwise), along with 95 or else from 1000 independent draws from the posterior distribution under vague independent normal prior on the log-scale and shape. The latter two methods better reflect the asymmetry of the estimates than the Wald confidence intervals.

Usage

tstab.gpd(
  xdat,
  thresh,
  method = c("wald", "profile", "post"),
  level = 0.95,
  plot = TRUE,
  ...
)

Arguments

xdat: a vector of observations
thresh: a vector of candidate thresholds at which to compute the estimates.
method: string indicating the method for computing confidence or credible intervals. Must be one of "wald", "profile" or "post".
level: confidence level of the intervals. Default to 0.95.
plot: logical; should parameter stability plots be displayed? Default to TRUE.
...: additional arguments passed to plot.

Value

a list with components

threshold: vector of numerical threshold values.
mle: matrix of modified scale and shape maximum likelihood estimates.
lower: matrix of lower bounds for the confidence or credible intervals.
upper: matrix of lower bounds for the confidence or credible intervals.
method: method for the confidence or coverage intervals.

plots of the modified scale and shape parameters, with pointwise confidence/credible intervals and an invisible data frame containing the threshold thresh and the modified scale and shape parameters.

Author

Leo Belzile

Examples

dat <- abs(rnorm(10000))
u <- qnorm(seq(0.9,0.99, by= 0.01))
tstab.gpd(xdat = dat, thresh = u)

if (FALSE) {
tstab.gpd(xdat = dat, thresh = u, method = "profile")
tstab.gpd(xdat = dat, thresh = u, method = "post")
}