spm_mle: Semiparametric maxima estimator of the extremal index

In ConstantinosChr/exdex: Estimation of the Extremal Index

Description

Calculates the semiparametric maxima estimator of the extremal index θ based on sliding or disjoint block maxima based on Northrop (2015).

Usage

spm_mle(data, b, sliding = TRUE, constrain = TRUE, conf = NULL,
  R = 1000)

Arguments

data	A numeric vector of raw data.
b	A numeric scalar. The block size.
sliding	A logical scalar indicating whether use sliding blocks (TRUE) or disjoint blocks (FALSE).
constrain	A logical scalar indicating whether or not to constrain the mle to lie in the interval (0, 1].
conf	A numeric scalar. If conf is supplied then the the standard error and conf% likelihood-based confidence interval for θ, and the standard error of the estimator of θ, are estimated using block bootstrapping, implemented by tsboot. See Northrop (2015) and references therein for more information.
R	An integer scalar. The number of bootstrap resamples used to estimate the standard error and confidence intervals. See tsboot.

Details

The extremal index θ is estimated using the semiparametric maxima estimator of Northrop (2015). If sliding = TRUE then the function uses sliding block maxima, that is, the largest value observed in all blocks of b observations, whereas if sliding = FALSE then disjoint block maxima, that is, the largest values in non-overlapping blocks of b observations, are used. If constrain = TRUE then if the raw estimate of the extremal index is greater than one then a value of 1 is returned. Otherwise (constrain = FALSE) the raw estimate is returned, even if it is greater than 1.

Value

A list containing

• theta_mle : The maximum likelihood estimate (MLE) of θ.

• theta_se : The estimated standard error of the MLE.

• theta_ci : (If conf is supplied) a numeric vector of length two giving lower and upper confidence limits for θ.

If conf is not supplied then only the MLE theta_mle is returned.

References

Northrop, P. J. (2015) An efficient semiparametric maxima estimator of the extremal index Extremes, 18(4), 585-603. http://dx.doi.org/10.1007/s10687-015-0221-5

See Also

kgaps_mle for maximum likelihood estimation of the extremal index θ using the K-gaps model.

Examples

spm_mle(newlyn, 20)
spm_mle(newlyn, 20, sliding = FALSE)

spm_mle(newlyn, 20, sliding = FALSE, conf = 95)
# When sliding = TRUE bootstrapping is slow
## Not run: 
spm_mle(newlyn, 20, conf = 95)

## End(Not run)

ConstantinosChr/exdex documentation built on May 14, 2019, 4:16 p.m.