confint.kgaps: Confidence intervals for the extremal index theta

Description Usage Arguments Details Value References Examples

Description

confint method for objects of class c("kgaps", "exdex"). Computes confidence intervals for θ 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 θ, which are symmetric about the point estimate, and (b) likelihood-based intervals.

Usage

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## S3 method for class '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 θ.

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 θ directly. If conf_scale = "log" then confidence intervals are first estimated for logθ and then transformed back to the θ-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.

Details

Two type of interval are calculated: (a) an interval based on the approximate large sample normality of the estimator of θ (if conf_scale = "theta") or of logθ (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.

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.

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

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u <- quantile(newlyn, probs = 0.90)
theta <- kgaps(newlyn, u)
confint(theta)

exdex documentation built on Aug. 6, 2019, 5:05 p.m.