Adaptation of Varty et al.'s metric-based threshold automated diagnostic for the independent and identically distributed case with no rounding.
Arguments
- xdat
- vector of observations 
- thresh
- vector of thresholds 
- B
- number of bootstrap replications 
- type
- string indicating scale, either - expfor exponential quantile-quantile plot as in Varty et al. (2021) or- ppfor probability-probability plot (uniform). The method- qqor expected quantile discrepancy (- eqd) corresponds to Murphy et al. (2024) with the quantiles on the generalized Pareto scale.
- dist
- string indicating norm, either - l1for absolute error or- l2for quadratic error
- uq
- logical; if - TRUE, generate bootstrap samples accounting for the sampling distribution of parameters
- neval
- number of points at which to estimate the metric. Default to 1000L 
- ci
- level of symmetric confidence interval. Default to 0.95 
Value
an invisible list with components
- thresh: scalar threshold minimizing criterion
- thresh0: vector of candidate thresholds
- metric: value of the metric criterion evaluated at each threshold
- type: argument- type
- dist: argument- dist
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.
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.
Murphy, C., Tawn, J. A., & Varty, Z. (2024). Automated Threshold Selection and Associated Inference Uncertainty for Univariate Extremes. Technometrics, 67(2), 215–224. <doi:10.1080/00401706.2024.2421744>