Heffernan-Tawn conditional extremes model

Formula: Y_j | X = x = a_j x + x^(b_j) Z_j for x > u

Usage

Evhpvr(X, u)

Arguments

X: An n x 2 matrix; column 1 conditions, on a standard Laplace or exponential-type scale.
u: Conditioning threshold applied to column 1.

Value

List with a, b, mu_z, sigma_z, estimate, nll, n_exceed, n, method.

Details

Fitted by Gaussian likelihood on the exceedance set. The slope a and the residual mean and sd are profiled out in closed form at every b, leaving a single bounded search for b: its stationary point is bracketed by a sign change of the profile derivative on a fixed grid and then bisected.

References

Heffernan & Tawn (2004), JRSS B 66(3):497-546.

Examples

set.seed(1)
Evhpvr(matrix(rnorm(40), 20, 2), u = 1)
#> $a
#> [1] 2373.588
#> 
#> $b
#> [1] 0.999
#> 
#> $mu_z
#> [1] -2374.902
#> 
#> $sigma_z
#> [1] 0.938139
#> 
#> $estimate
#> [1] 2373.588
#> 
#> $nll
#> [1] 0.8054906
#> 
#> $n_exceed
#> [1] 3
#> 
#> $n
#> [1] 20
#> 
#> $method
#> [1] "Heffernan-Tawn conditional extremes model"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"