Score and likelihood ratio tests fit of equality of shape over multiple thresholds

The function returns a P-value path for the score testand/or likelihood ratio test for equality of the shape parameters over multiple thresholds under the generalized Pareto model.

Usage

NC.diag(
  xdat,
  u,
  GP.fit = c("Grimshaw", "nlm", "optim", "ismev"),
  do.LRT = FALSE,
  size = NULL,
  plot = TRUE,
  ...,
  xi.tol = 0.001
)

Arguments

xdat: numeric vector of raw data
u: m-vector of thresholds (sorted from smallest to largest)
GP.fit: function used to optimize the generalized Pareto model.
do.LRT: boolean indicating whether to perform the likelihood ratio test (in addition to the score test)
size: level at which a horizontal line is drawn on multiple threshold plot
plot: logical; if TRUE, return a plot of p-values against threshold.
...: additional parameters passed to plot
xi.tol: numerical tolerance for threshold distance; if the absolute value of xi1.hat is less than xi.tol use linear interpolation to evaluate score vectors, expected Fisher information matrices, Hessians

Value

a plot of P-values for the test at the different thresholds u

Details

The default method is 'Grimshaw' using the reduction of the parameters to a one-dimensional maximization. Other options are one-dimensional maximization of the profile the nlm function or optim. Two-dimensional optimisation using 2D-optimization ismev using the routine from gpd.fit from the ismev library, with the addition of the algebraic gradient. The choice of GP.fit should make no difference but the options were kept. Warning: the function will not recover from failure of the maximization routine, returning various error messages.

References

Grimshaw (1993). Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution, Technometrics, 35(2), 185--191.

Northrop & Coleman (2014). Improved threshold diagnostic plots for extreme value analyses, Extremes, 17(2), 289--303.

Wadsworth & Tawn (2012). Likelihood-based procedures for threshold diagnostics and uncertainty in extreme value modelling, J. R. Statist. Soc. B, 74(3), 543--567.

Author

Paul J. Northrop and Claire L. Coleman

Examples

if (FALSE) {
data(nidd)
u <- seq(65,90, by = 1L)
NC.diag(nidd, u, size = 0.05)
}