# Extrapolate coverage and width using sub-sampled bootstrap confidence intervals. Given a set of bootstrap confidence intervals calculated across sub-samples with different numbers of replications, extrapolates confidence interval coverage and width of bootstrap confidence intervals to a specified (larger) number of bootstraps. The function also calculates the associated Monte Carlo standard errors. The confidence interval percentage is based on how you calculated the lower and upper bounds. ```r extrapolate_coverage( data, CI_subsamples, true_param, B_target = Inf, criteria = c("coverage", "width"), winz = Inf, nested = FALSE, format = "wide", width_trim = 0, cover_na_val = NA, width_na_val = NA ) ``` ## Arguments - `data`: data frame or tibble containing the simulation results. - `CI_subsamples`: list or name of column from `data` containing list of confidence intervals calculated based on sub-samples with different numbers of replications. - `true_param`: vector or name of column from `data` containing corresponding true parameters. - `B_target`: number of bootstrap replications to which the criteria should be extrapolated, with a default of `B = Inf`. - `criteria`: character or character vector indicating the performance criteria to be calculated, with possible options `"coverage"` and `"width"`. - `winz`: numeric value for winsorization constant. If set to a finite value, estimates will be winsorized at the constant multiple of the inter-quartile range below the 25th percentile or above the 75th percentile of the distribution. For instance, setting `winz = 3` will truncate estimates that fall below P25 - 3 * IQR or above P75 + 3 * IQR. - `nested`: logical value controlling the format of the output. If `FALSE` (the default), then the results will be returned as a data frame with rows for each distinct number of bootstraps. If `TRUE`, then the results will be returned as a data frame with a single row, with each performance criterion containing a nested data frame. - `format`: character string controlling the format of the output when `CI_subsamples` has results for more than one type of confidence interval. If `"wide"` (the default), then each performance criterion will have a separate column for each CI type. If `"long"`, then each performance criterion will be a single variable, with separate rows for each CI type. - `width_trim`: numeric value specifying the trimming percentage to use when summarizing CI widths across replications from a single set of bootstraps, with a default of 0.0 (i.e., use the regular arithmetic mean). - `cover_na_val`: numeric value to use for calculating coverage if bootstrap CI end-points are missing. Default is `NA`. - `width_na_val`: numeric value to use for calculating width if bootstrap CI end-points are missing. Default is `NA`. ## Returns A tibble containing the number of simulation iterations, performance criteria estimate(s) and the associated MCSE. ## Examples ```r dgp <- function(N, mu, nu) { mu + rt(N, df = nu) } estimator <- function( dat, B_vals = c(49,59,89,99), m = 4, trim = 0.1 ) { # compute estimate and standard error N <- length(dat) est <- mean(dat, trim = trim) se <- sd(dat) / sqrt(N) # compute booties booties <- replicate(max(B_vals), { x <- sample(dat, size = N, replace = TRUE) data.frame( M = mean(x, trim = trim), SE = sd(x) / sqrt(N) ) }, simplify = FALSE) |> dplyr::bind_rows() # confidence intervals for each B_vals CIs <- bootstrap_CIs( boot_est = booties$M, boot_se = booties$SE, est = est, se = se, CI_type = c("normal","basic","student","percentile"), B_vals = B_vals, reps = m, format = "wide-list" ) res <- data.frame( est = est, se = se ) res$CIs <- CIs res } #' build a simulation driver function simulate_bootCIs <- bundle_sim( f_generate = dgp, f_analyze = estimator ) boot_results <- simulate_bootCIs( reps = 50, N = 20, mu = 2, nu = 3, B_vals = seq(49, 199, 50), ) extrapolate_coverage( data = boot_results, CI_subsamples = CIs, true_param = 2 ) extrapolate_coverage( data = boot_results, CI_subsamples = CIs, true_param = 2, B_target = 999, format = "long" ) ``` ## References \insertRef boos2000MonteCarloEvaluationsimhelpers

extrapolate_coverage function