Threshold selection by local variance of the GPD estimates

Formula: argmin_u Var(log sigma*_u, xi_u)

Usage

Evtsthr(x, u_grid = NULL, window = 3)

Arguments

x

Sample.

u_grid

Candidate thresholds, or NULL for the 50th to 90th sample percentiles in nine steps.

window

Number of consecutive thresholds per variance.

Value

List with u_star, score, estimate, u, scores, xi, mod_scale, n, method.

Details

A GPD fitted above u0 implies, for any higher u, sigma_u = sigma_u0 + xi (u - u0), so the MODIFIED scale sigma*_u = sigma_u - xi u and the shape xi are both constant in u once the model holds. The threshold chosen is the one whose forward window of fits has the smallest combined variance of log sigma* and xi – the first place the parameters stop drifting.

References

Northrop & Coleman (2014), Extremes 17(2):289-303.

Examples

set.seed(1)
Evtsthr(rexp(200))
#> $u_star
#> [1] 1.00139
#> 
#> $score
#> [1] 0.0008868064
#> 
#> $estimate
#> [1] 1.00139
#> 
#> $u
#> [1] 0.7674910 0.8268357 1.0013904 1.1067204 1.2349351 1.3503761 1.5721328
#> [8] 1.8421319 2.1750062
#> 
#> $scores
#> [1] 0.0117638222 0.0130863430 0.0008868064 0.0113861357 0.0083197552
#> [6] 0.0109679497 0.0520633214
#> 
#> $xi
#> [1] -0.090116576 -0.129589743 -0.053105446 -0.068407983 -0.071336756
#> [6] -0.130284081 -0.110240303 -0.067353483  0.006683128
#> 
#> $mod_scale
#> [1] 1.0042671 1.1117576 0.9075161 0.9472171 0.9569099 1.1334773 1.0705336
#> [8] 0.9336347 0.6955195
#> 
#> $n
#> [1] 200
#> 
#> $method
#> [1] "threshold selection by local variance of GPD estimates"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"