R/exact_bootstrap.R

In exactamente: Explore the Exact Bootstrap Method

#' @title Performs an Exact Bootstrap with Summary Statistics
#' @description Performs an exact bootstrap method on small datasets and returns
#' a set of summary statistics. This function implements a popular variant of exact
#' bootstrapping where the total number of combinations is expressed as N^N
#' (i.e., the vector c(1 ,2, 7) has 3^3 = 27 combinations rather than the 10
#' combinations obtained from exact case bootstrapping), giving more weight to a
#' resample with larger variation, thus potentially increasing the bootstrap
#' estimate's accuracy. This technique is described in Kisielinska (2013).
#' @param data A numeric vector of data points.
#' @param check_size A logical value indicating whether to check if the size of the
#' dataset is less than 10. Default is TRUE.
#' @param anon A function to compute the sample statistic for each bootstrap
#' sample. Default is the mean function.
#' @param lb Lower bound for the confidence interval. Default is 0.025.
#' @param ub Upper bound for the confidence interval. Default is 0.975.
#' @param density_args Pass additional arguments to stats::density
#' @return A list with two elements: \itemize{
#'  \item dens: a density estimate of the bootstrap sample statistics,
#'  \item stats: a list of summary statistics including number of resamples, mode,
#'  median, mean, standard deviation, lower confidence interval (lCI), and upper
#'  confidence interval (uCI).}
#' @examples
#' set.seed(123)
#' data <- rnorm(5)
#' result <- exact_bootstrap(data)
#' summary(result)
#' plot(result)
#' @seealso \code{\link{plot.extboot}}, \code{\link{summary.extboot}}
#' @references
#' Kisielinska, J. (2013). The exact bootstrap method shown on the example of the mean and variance estimation. Computational Statistics, 28, 1061–1077. \doi{https://doi.org/10.1007/s00180-012-0350-0}
#' @export
exact_bootstrap <- function(data, check_size = TRUE, anon = function(x)(mean(x)),
                            lb = 0.025, ub = 0.975, density_args) {
  n <- length(data)
  if (check_size == TRUE & n > 9) stop("This function only works for datasets
                                        with less than 10 observations.")

  if(!(is.vector(data) & is.numeric(data))) stop("data should be a numeric vector.")

  # Generate all possible bootstrap samples.
  bootstrap_samples <- expand.grid(rep(list(data), n))

  # Compute the sample stat for each bootstrap sample.
  bootstrap_stats <- apply(bootstrap_samples, 1, anon)

  # Process bootstrap stats
  result <- process_bootstrap_stats(bootstrap_stats = bootstrap_stats,
                                    density_args = density_args,
                                    lb = lb, ub = ub)

  # Assign "extboot" class
  class(result) <- "extboot"

  return(result)
}


#' Plot Method for 'extboot' Class
#'
#' @description Creates a plot of the density estimates of the bootstrap sample statistics
#' returned from the \code{\link{exact_bootstrap}} function.
#' @param x An object of class 'extboot', usually the output of the \code{\link{exact_bootstrap}} function.
#' @param title A plot title. Default is "Exact Bootstrap Distribution".
#' @param ... Additional parameters (currently ignored).
#' @return A ggplot object showing the density estimates of the bootstrap sample statistic.
#' @seealso \code{\link{exact_bootstrap}}, \code{\link{summary.extboot}}
#' @examples
#' set.seed(123)
#' data <- rnorm(5)
#' result <- exact_bootstrap(data)
#' plot(result)
#' @export
plot.extboot <- function(x, title = "Exact Bootstrap Distribution", ...) {
  if(methods::is(x) != "extboot")
    stop("x must be an object of class extboot")
  boot_plot(x, title = title)
}

#' Summary Method for 'extboot' Class
#'
#' @description Creates a summary table of the summary statistics computed in the
#' \code{\link{exact_bootstrap}} function.
#' @param object An object of class 'extboot', usually the output of the \code{\link{exact_bootstrap}} function.
#' @param ... Additional parameters (currently ignored).
#' @return A data.frame containing the summary statistics.
#' @seealso \code{\link{exact_bootstrap}}, \code{\link{plot.extboot}}
#' @examples
#' set.seed(123)
#' data <- rnorm(5)
#' result <- exact_bootstrap(data)
#' summary(result)
#' @export
summary.extboot <- function(object, ...) {
  if(methods::is(object) != "extboot")
    stop("object must be an object of class extboot")
  summary_table <- xboot_summary(object)
  return(summary_table)
}