dgaps_imt: Information matrix test under the D-gaps model
In exdex: Estimation of the Extremal Index

dgaps_imt

R Documentation

Information matrix test under the `D`-gaps model

Description

Performs an information matrix test (IMT) to diagnose misspecification of the D-gaps model of Holesovsky and Fusek (2020).

Usage

dgaps_imt(data, u, D = 1, inc_cens = TRUE)

Arguments

data

A numeric vector or numeric matrix of raw data. If data is a matrix then the log-likelihood is constructed as the sum of (independent) contributions from different columns. A common situation is where each column relates to a different year.

If data contains missing values then split_by_NAs is used to divide the data into sequences of non-missing values.

u, D

Numeric vectors. u is a vector of extreme value thresholds applied to data. D is a vector of values of the left-censoring parameter D, as defined in Holesovsky and Fusek (2020). See dgaps.

Any values in u that are greater than all the observations in data will be removed without a warning being given.

inc_cens

A logical scalar indicating whether or not to include contributions from right-censored inter-exceedance times, relating to the first and last observations. See dgaps.

Details

The general approach follows Suveges and Davison (2010). The D-gaps IMT is performed a over grid of all combinations of threshold and D in the vectors u and D. If the estimate of \theta is 0 then the IMT statistic, and its associated p-value is NA.

Value

An object (a list) of class c("dgaps_imt", "exdex") containing

`imt`	A `length(u)` by `length(D)` numeric matrix. Column i contains, for `D` = `D[i]`, the values of the information matrix test statistic for the set of thresholds in `u`. The column names are the values in `D`. The row names are the approximate empirical percentage quantile levels of the thresholds in `u`.
`p`	A `length(u)` by `length(D)` numeric matrix containing the corresponding `p`-values for the test.
`theta`	A `length(u)` by `length(D)` numeric matrix containing the corresponding estimates of `\theta`.
`u`, `D`	The input `u` and `D`.

References

Holesovsky, J. and Fusek, M. Estimation of the extremal index using censored distributions. Extremes 23, 197-213 (2020). \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10687-020-00374-3")}

Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, Annals of Applied Statistics, 4(1), 203-221. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/09-AOAS292")}

Examples

### Newlyn sea surges

u <- quantile(newlyn, probs = seq(0.1, 0.9, by = 0.1))
imt <- dgaps_imt(newlyn, u = u, D = 1:5)

### S&P 500 index

u <- quantile(sp500, probs = seq(0.1, 0.9, by = 0.1))
imt <- dgaps_imt(sp500, u = u, D = 1:5)

### Cheeseboro wind gusts (a matrix containing some NAs)

probs <- c(seq(0.5, 0.98, by = 0.025), 0.99)
u <- quantile(cheeseboro, probs = probs, na.rm = TRUE)
imt <- dgaps_imt(cheeseboro, u = u, D = 1:5)

### Uccle July temperatures

probs <- c(seq(0.7, 0.98, by = 0.025), 0.99)
u <- quantile(uccle720m, probs = probs, na.rm = TRUE)
imt <- dgaps_imt(uccle720m, u = u, D = 1:5)

exdex documentation built on May 29, 2024, 2:15 a.m.