vmetric.diag: Metric-based threshold selection

In mev: Modelling of Extreme Values

Metric-based threshold selection

Description

Adaptation of Varty et al.'s metric-based threshold automated diagnostic for the independent and identically distributed case with no rounding.

Usage

vmetric.diag(
  xdat,
  thresh,
  B = 199L,
  type = c("qq", "pp"),
  dist = c("l1", "l2"),
  neval = 1000L,
  ci = 0.95
)

Arguments

xdat	vector of observations
thresh	vector of thresholds
B	number of bootstrap replications
type	string indicating scale, either qq for exponential quantile-quantile plot or pp for probability-probability plot (uniform)
dist	string indicating norm, either l1 for absolute error or l2 for quadratic error
neval	number of points at which to estimate the metric. Default to 1000L
ci	level of symmetric confidence interval. Default to 0.95

Details

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.

Value

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

References

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

mev documentation built on Sept. 11, 2024, 8:14 p.m.