choose_uk {exdex}

Threshold u and runs parameter K diagnostic for the K-gaps estimator

Description

Creates data for a plot to aid the choice of the threshold and run parameter K for the K-gaps estimator (see kgaps). plot.choose_uk creates the plot.

Usage

choose_uk(data, u, k = 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, k

Numeric vectors. u is a vector of extreme value thresholds applied to data. k is a vector of values of the run parameter K, as defined in Suveges and Davison (2010). See kgaps for more details.

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 censored inter-exceedance times, relating to the first and last observations. See Attalides (2015) for details.

Details

For each combination of threshold in u and K in k the functions kgaps and kgaps_imt are called in order to estimate \theta and to perform the information matrix test of Suveges and Davison (2010).

Value

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

imt

an object of class c("kgaps_imt", "exdex") returned from kgaps_imt.

theta

a length(u) by length(k) matrix. Element (i,j) of theta contains an object (a list) of class c("kgaps", "exdex"), a result of a call kgaps(data, u[j], k[i]) to kgaps.

References

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

Attalides, N. (2015) Threshold-based extreme value modelling, PhD thesis, University College London. https://discovery.ucl.ac.uk/1471121/1/Nicolas_Attalides_Thesis.pdf

See Also

kgaps for maximum likelihood estimation of the extremal index \theta using the K-gaps model.

kgaps_imt for the information matrix test under the K-gaps model

plot.choose_uk to produce the diagnostic plot.

Examples

### S&P 500 index

# Multiple thresholds and run parameters
u <- quantile(sp500, probs = seq(0.1, 0.9, by = 0.1))
imt_theta <- choose_uk(sp500, u = u, k = 1:5)
plot(imt_theta)
plot(imt_theta, uprob = TRUE)
plot(imt_theta, y = "theta")

# One run parameter K, many thresholds u
u <- quantile(sp500, probs = seq(0.1, 0.9, by = 0.1))
imt_theta <- choose_uk(sp500, u = u, k = 1)
plot(imt_theta)
plot(imt_theta, y = "theta")

# One threshold u, many run parameters K
u <- quantile(sp500, probs = 0.9)
imt_theta <- choose_uk(sp500, u = u, k = 1:5)
plot(imt_theta)
plot(imt_theta, y = "theta")

### Newlyn sea surges

u <- quantile(newlyn, probs = seq(0.1, 0.9, by = 0.1))
imt_theta <- choose_uk(newlyn, u = u, k = 1:5)
plot(imt_theta, uprob = TRUE)

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

probs <- c(seq(0.5, 0.95, by = 0.05), 0.99)
u <- quantile(cheeseboro, probs = probs, na.rm = TRUE)
imt_theta <- choose_uk(cheeseboro, u, k = 1:6)
plot(imt_theta, uprob = FALSE, lwd = 2)

### Uccle July temperatures

probs <- c(seq(0.7, 0.95, by = 0.05), 0.99)
u <- quantile(uccle720m, probs = probs, na.rm = TRUE)
imt_theta <- choose_uk(uccle720m, u, k = 1:5)
plot(imt_theta, uprob = TRUE, lwd = 2)