R: Wadsworth's univariate and bivariate exponential threshold...
W.diag
R Documentation
Wadsworth's univariate and bivariate exponential threshold diagnostics
Description
Function to produce diagnostic plots and test statistics for the
threshold diagnostics exploiting structure of maximum likelihood estimators
based on the non-homogeneous Poisson process likelihood
string specifying whether the univariate or bivariate diagnostic should be used. Either nhpp
for the univariate model, exp (invexp) for the bivariate exponential model with rate (inverse rate) parametrization. See details.
u
optional; vector of candidate thresholds.
k
number of thresholds to consider (if u unspecified).
q1
lowest quantile for the threshold sequence.
q2
upper quantile limit for the threshold sequence (q2 itself is not used as a threshold,
but rather the uppermost threshold will be at the q2-1/k quantile).
par
parameters of the NHPP likelihood. If missing, the fpot routine will be run to obtain values
M
number of superpositions or "blocks" / "years" the process corresponds to (can affect the optimization)
nbs
number of simulations used to assess the null distribution of the LRT, and produce the p-value
alpha
significance level of the LRT
plots
vector of strings indicating which plots to produce; LRT= likelihood ratio test, WN = white noise, PS = parameter stability
UseQuantiles
logical; use quantiles as the thresholds in the plot?
pmar
vector of length 4 giving the arguments for the plot margins in par(mar=c(*,*,*,*)).
tikz
logical; if TRUE, axis labels are replaced with LaTeX code
...
additional parameters passed to plot.
Details
The function is a wrapper for the univariate (non-homogeneous Poisson process model) and bivariate exponential dependence model.
For the latter, the user can select either the rate or inverse rate parameter (the inverse rate parametrization works better for uniformity
of the p-value distribution under the LR test.
There are two options for the bivariate diagnostic: either provide pairwise minimum of marginally
exponentially distributed margins or provide a n times 2 matrix with the original data, which
is transformed to exponential margins using the empirical distribution function.
Value
plots of the requested diagnostics and a list with components
MLE maximum likelihood estimates from all thresholds
Cov joint asymptotic covariance matrix for xi, eta or 1/eta.
WN values of the white noise process.
LRT values of the likelihood ratio test statistic vs threshold.
pval P-value of the likelihood ratio test.
k final number of thresholds used.
thresh threshold selected by the likelihood ratio procedure.
mle.u maximum likelihood estimates from selected threshold.
Author(s)
Jennifer L. Wadsworth
References
Wadsworth, J.L. (2016). Exploiting Structure of Maximum Likelihood Estimators for Extreme Value Threshold Selection, Technometrics, 58(1), 116-126, http://dx.doi.org/10.1080/00401706.2014.998345.