Adaptation of Varty et al.'s metric-based threshold automated diagnostic for the independent and identically distributed case with no rounding.
vmetric.diag(
xdat,
thresh,
B = 199L,
type = c("qq", "pp"),
dist = c("l1", "l2"),
neval = 1000L,
ci = 0.95
)an invisible list with components
thresh: scalar threshold minimizing criterion
cthresh: vector of candidate thresholds
metric: value of the metric criterion evaluated at each threshold
type: argument type
dist: argument dist
vector of observations
vector of thresholds
number of bootstrap replications
string indicating scale, either qq for exponential quantile-quantile plot or pp for probability-probability plot (uniform)
string indicating norm, either l1 for absolute error or l2 for quadratic error
number of points at which to estimate the metric. Default to 1000L
level of symmetric confidence interval. Default to 0.95
The algorithm proceeds by first computing the maximum likelihood algorithm and then simulating datasets from replication with parameters drawn from a bivariate normal approximation to the maximum likelihood estimator distribution.
For each bootstrap sample, we refit the model and convert the quantiles to exponential or uniform variates. The mean absolute or mean squared distance is calculated on these. The threshold returned is the one with the lowest value of the metric.
Varty, Z. and J.A. Tawn and P.M. Atkinson and S. Bierman (2021+), Inference for extreme earthquake magnitudes accounting for a time-varying measurement process