tstab.gpd {mev}

Parameter stability plots for peaks-over-threshold

Description

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,
  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(s)

Leo Belzile

See Also

gpd.fitrange

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)
## Not run: 
tstab.gpd(xdat = dat, thresh = u, method = "profile")
tstab.gpd(xdat = dat, thresh = u, method = "post")

## End(Not run)