exdex (version 1.0.1)

confint.kgaps: Confidence intervals for the extremal index \(\theta\)

Description

confint method for objects of class c("kgaps", "exdex"). Computes confidence intervals for \(\theta\) based on an object returned from kgaps. Two types of interval may be returned: (a) intervals based on approximate large-sample normality of the estimator of \(\theta\), which are symmetric about the point estimate, and (b) likelihood-based intervals.

Usage

# S3 method for kgaps
confint(object, parm = "theta", level = 0.95,
  interval_type = c("both", "norm", "lik"), conf_scale = c("theta",
  "log"), constrain = TRUE, ...)

Arguments

object

An object of class c("kgaps", "exdex"), returned by kgaps.

parm

Specifies which parameter is to be given a confidence interval. Here there is only one option: the extremal index \(\theta\).

level

The confidence level required. A numeric scalar in (0, 1).

interval_type

A character scalar: "norm" for intervals of type (a), "lik" for intervals of type (b).

conf_scale

A character scalar. If interval_type = "norm" then conf_scale determines the scale on which we use approximate large-sample normality of the estimator to estimate confidence intervals.

If conf_scale = "theta" then confidence intervals are estimated for \(\theta\) directly. If conf_scale = "log" then confidence intervals are first estimated for \(\log\theta\) and then transformed back to the \(\theta\)-scale.

constrain

A logical scalar. If constrain = TRUE then any confidence limits that are greater than 1 are set to 1, that is, they are constrained to lie in (0, 1]. Otherwise, limits that are greater than 1 may be obtained. If constrain = TRUE then any lower confidence limits that are less than 0 are set to 0.

...

Further arguments. None are used currently.

Value

A matrix with columns giving the lower and upper confidence limits. These are labelled as (1 - level)/2 and 1 - (1 - level)/2 in % (by default 2.5% and 97.5%). The row names indicate the type of interval: norm for intervals based on large sample normality and lik for likelihood-based intervals.

Details

Two type of interval are calculated: (a) an interval based on the approximate large sample normality of the estimator of \(\theta\) (if conf_scale = "theta") or of \(\log\theta\) (if conf_scale = "log") and (b) a likelihood-based interval, based on the approximate large sample chi-squared, with 1 degree of freedom, distribution of the log-likelihood ratio statistic.

References

Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, The Annals of Applied Statistics, 4(1), 203-221. https://doi.org/10.1214/09-AOAS292

Examples

# NOT RUN {
u <- quantile(newlyn, probs = 0.90)
theta <- kgaps(newlyn, u)
confint(theta)
# }