# confint.kgaps: Confidence intervals for the extremal index theta In exdex: Estimation of the Extremal Index

## 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

 ```1 2 3 4``` ```## 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

 ```1 2 3``` ```u <- quantile(newlyn, probs = 0.90) theta <- kgaps(newlyn, u) confint(theta) ```

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