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.
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 - scaleor- 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.
