# Threshold $u$ and runs parameter $K$ diagnostic for the $K$-gaps estimator 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. ```r 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. ## Returns 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`. ## 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). ## Examples ```r ### 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) ``` ## References Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, **Annals of Applied Statistics**, 4 (1), 203-221. tools:::Rd_expr_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](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.

choose_uk function