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% confidence/credible intervals obtained using Wald or profile confidence intervals, 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,
  which = c("scale", "shape"),
  changepar = 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.
which: character vector with elements scale or shape
changepar: logical; if TRUE, changes the graphical parameters.
...: 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.

Note

The function is hard coded to prevent fitting a generalized Pareto distribution to samples of size less than 10. If the estimated shape parameters are all on the boundary of the parameter space (meaning \(\hat{\xi}=-1\)), then the plots return one-sided confidence intervals for both the modified scale and shape parameters: these typically suggest that the chosen thresholds are too high for estimation to be reliable.

Author

Leo Belzile

Examples

dat <- abs(rnorm(10000))
u <- qnorm(seq(0.9,0.99, by= 0.01))
par(mfrow = c(1,2))
tstab.gpd(xdat = dat, thresh = u, changepar = FALSE)

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