Confidence intervals for the extremal index \(\theta\) for "dgaps" objects

Source: R/confidence_intervals.R

confint method for objects of class c("dgaps", "exdex"). Computes confidence intervals for \(\theta\) based on an object returned from dgaps. 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. The plot method plots the log-likelihood for \(\theta\), with the required confidence interval indicated on the plot.

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

# S3 method for confint_dgaps
plot(x, ...)

# S3 method for confint_dgaps
print(x, ...)

Arguments

object

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

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.

se_type

A character scalar. Should the confidence intervals for the interval_type = "norm" use the estimated standard error based on the observed information or based on the expected information?

...

plot.confint_dgaps: further arguments passed to plot.confint.

print.confint_dgaps: further arguments passed to print.default.

x

an object of class c("confint_dgaps", "exdex"), a result of a call to confint.dgaps.

Value

A list of class c("confint_dgaps", "exdex") containing the following components.

cis

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.

call

The call to spm.

object

The input object object.

level

The input level.

plot.confint_dgaps: nothing is returned.

print.confint_dgaps: the argument x, invisibly.

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.

print.confint_dgaps prints the matrix of confidence intervals for \(\theta\).

References

Holesovsky, J. and Fusek, M. Estimation of the extremal index using censored distributions. Extremes 23, 197-213 (2020). doi:10.1007/s10687-020-00374-3

See also

dgaps for estimation of the extremal index \(\theta\) using a semiparametric maxima method.

Examples

u <- quantile(newlyn, probs = 0.90)
theta <- dgaps(newlyn, u)
cis <- confint(theta)
cis
#>          2.5 %    97.5 %
#> norm 0.3406122 0.4345061
#> lik  0.3420138 0.4357397
plot(cis)