Pickands estimator of the extreme-value index

Pickands (1975): the log spacing ratio at k, 2k, 4k over log 2. Consistent for EVERY real xi – heavy, light and bounded tails alike – because it uses spacings rather than logs of levels. The price is efficiency: its asymptotic variance (de Haan-Ferreira Thm. 3.3.5; 3/(4 log^2 2) at xi = 0) is far above Hill's xi^2 where both are valid, so Hill wins when xi > 0 is known and Pickands is the tool when the SIGN of xi is in question.

Usage

morie_evt_pickands(x, k = NULL)

Arguments

x

sample.

k

spacing parameter, 4k <= n; n %/% 8 when NULL.

Value

list: xi, se, k, order_stats_used, valid_for, versus_hill, n, method.

References

Pickands (1975), Annals of Statistics 3:119-131; de Haan and Ferreira (2006), Thm. 3.3.5.

Examples

set.seed(1)
morie_evt_pickands(stats::rnorm(400))$xi
#> [1] -0.6714319