| Title: | Explore the Exact Bootstrap Method |
| Version: | 0.1.1 |
| Description: | Researchers often use the bootstrap to understand a sample drawn from a population with unknown distribution. The exact bootstrap method is a practical tool for exploring the distribution of small sample size data. For a sample of size n, the exact bootstrap method generates the entire space of n to the power of n resamples and calculates all realizations of the selected statistic. The 'exactamente' package includes functions for implementing two bootstrap methods, the exact bootstrap and the regular bootstrap. The exact_bootstrap() function applies the exact bootstrap method following methodologies outlined in Kisielinska (2013) <doi:10.1007/s00180-012-0350-0>. The regular_bootstrap() function offers a more traditional bootstrap approach, where users can determine the number of resamples. The e_vs_r() function allows users to directly compare results from these bootstrap methods. To augment user experience, 'exactamente' includes the function exactamente_app() which launches an interactive 'shiny' web application. This application facilitates exploration and comparison of the bootstrap methods, providing options for modifying various parameters and visualizing results. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| URL: | https://github.com/mightymetrika/exactamente |
| BugReports: | https://github.com/mightymetrika/exactamente/issues |
| Imports: | ggplot2, methods, shiny, shinythemes |
| Suggests: | testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | no |
| Packaged: | 2023-08-29 15:18:43 UTC; Administrator |
| Author: | Mackson Ncube [aut, cre], mightymetrika, LLC [cph, fnd] |
| Maintainer: | Mackson Ncube <macksonncube.stats@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2023-08-29 17:00:05 UTC |
Plot Bootstrap Distributions
Description
Generates a plot of the density estimates of a bootstrap distribution.
Usage
boot_plot(dens, title = "Distribution")
Arguments
dens |
An object of class 'exboot', or 'regboot' |
title |
A plot title |
Value
A ggplot object showing the density estimates of a bootstrap sample statistic.
See Also
Compare Bootstrap Distributions
Description
This function generates a plot comparing the density estimates of the exact and regular bootstrap distributions.
Usage
compare_bootstrap(
exact_bootstrap_distribution,
regular_bootstrap_distribution,
title = "Comparison of Bootstrap Distributions"
)
Arguments
exact_bootstrap_distribution |
An named list returned from exact_bootstrap() with components dens$x (the coordinates of the points where the density is estimated) and y (the estimated density values), representing the density estimate of the exact bootstrap sample statistic. |
regular_bootstrap_distribution |
An named list returned from reg_bootstrap() with components dens$x (the coordinates of the points where the density is estimated) and y (the estimated density values), representing the density estimate of the regular bootstrap sample statistic. |
title |
Plot title |
Value
A ggplot object showing the density estimates of the exact and regular bootstrap sample statistics, with different colors used to distinguish between the two.
Examples
set.seed(123)
data <- rnorm(5)
exact_bootstrap_result <- exact_bootstrap(data)
regular_bootstrap_result <- reg_bootstrap(data)
compare_bootstrap(exact_bootstrap_result,
regular_bootstrap_result)
Compare Exact Bootstrap vs Regular Bootstrap
Description
This function runs the exact and regular bootstrap functions on a dataset, summarizes the results, and provides a comparative plot. It provides a convenient way to compare these two methods of bootstrapping.
Usage
e_vs_r(
data,
n_bootstraps = 10000,
check_size = TRUE,
anon = function(x) (mean(x)),
lb = 0.025,
ub = 0.975,
density_args,
title = "Comparison of Bootstrap Distributions"
)
Arguments
data |
A numeric vector of data values to be bootstrapped. |
n_bootstraps |
The number of bootstrap samples to generate. Defaults to 10000. |
check_size |
Logical indicating if a check should be performed to ensure the dataset has less than 10 observations for the exact bootstrap. Defaults to TRUE. |
anon |
An anonymous function to compute the statistic of interest on each bootstrap sample. Defaults to mean. |
lb |
Lower bound for the confidence interval. Defaults to 0.025. |
ub |
Upper bound for the confidence interval. Defaults to 0.975. |
density_args |
Pass additional arguments to stats::density |
title |
Plot title |
Value
A list containing two items:
summary_table: A summary table containing the mode, median, mean, standard deviation, and confidence interval for each bootstrap method.
comp_plot: A ggplot object comparing the bootstrap distributions.
Examples
set.seed(123)
data <- rnorm(5)
results <- e_vs_r(data)
print(results$summary_table)
print(results$comp_plot)
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).
Usage
exact_bootstrap(
data,
check_size = TRUE,
anon = function(x) (mean(x)),
lb = 0.025,
ub = 0.975,
density_args
)
Arguments
data |
A numeric vector of data points. |
check_size |
A logical value indicating whether to check if the size of the dataset is less than 10. Default is TRUE. |
anon |
A function to compute the sample statistic for each bootstrap sample. Default is the mean function. |
lb |
Lower bound for the confidence interval. Default is 0.025. |
ub |
Upper bound for the confidence interval. Default is 0.975. |
density_args |
Pass additional arguments to stats::density |
Value
A list with two elements:
dens: a density estimate of the bootstrap sample statistics,
stats: a list of summary statistics including number of resamples, mode, median, mean, standard deviation, lower confidence interval (lCI), and upper confidence interval (uCI).
References
Kisielinska, J. (2013). The exact bootstrap method shown on the example of the mean and variance estimation. Computational Statistics, 28, 1061–1077. doi:10.1007/s00180-012-0350-0
See Also
Examples
set.seed(123)
data <- rnorm(5)
result <- exact_bootstrap(data)
summary(result)
plot(result)
exactamente_app: Interactive Shiny App for Exploring Bootstrap Methods
Description
Launches a Shiny app to interactively explore and compare Exact and Regular bootstrap methods and All. The app provides a user-friendly interface, allowing users to modify various parameters associated with each bootstrap method, visualize the results, and understand the differences between the methods.
Usage
exactamente_app()
Value
A shinyApp object representing the running Shiny application. This function is primarily called for its side effects, which include the launching and running of the Shiny app.
Examples
if(interactive()){
exactamente_app()
}
Plot Method for 'extboot' Class
Description
Creates a plot of the density estimates of the bootstrap sample statistics
returned from the exact_bootstrap function.
Usage
## S3 method for class 'extboot'
plot(x, title = "Exact Bootstrap Distribution", ...)
Arguments
x |
An object of class 'extboot', usually the output of the |
title |
A plot title. Default is "Exact Bootstrap Distribution". |
... |
Additional parameters (currently ignored). |
Value
A ggplot object showing the density estimates of the bootstrap sample statistic.
See Also
exact_bootstrap, summary.extboot
Examples
set.seed(123)
data <- rnorm(5)
result <- exact_bootstrap(data)
plot(result)
Plot Method for 'regboot' Class
Description
Creates a plot of the density estimates of the bootstrap sample statistics
returned from the reg_bootstrap function.
Usage
## S3 method for class 'regboot'
plot(x, title = "Regular Bootstrap Distribution", ...)
Arguments
x |
An object of class 'regboot', usually the output of the |
title |
A plot title. Default is "Regular Bootstrap Distribution". |
... |
Additional parameters (currently ignored). |
Value
A ggplot object showing the density estimates of the bootstrap sample statistic.
See Also
reg_bootstrap, summary.regboot
Examples
set.seed(123)
data <- rnorm(5)
result <- reg_bootstrap(data)
plot(result)
Process Bootstrap Statistics
Description
This function takes in bootstrap statistics and additional arguments to compute the density estimate of the bootstrap statistic, the number of resamples, the mode, median, mean, standard deviation, and confidence interval. It returns a list containing the density estimate and summary statistics.
Usage
process_bootstrap_stats(
bootstrap_stats = bootstrap_stats,
density_args = density_args,
lb = lb,
ub = ub
)
Arguments
bootstrap_stats |
A numeric vector of bootstrap statistics. |
density_args |
A list of additional arguments to be passed to the density function. Default is NULL. |
lb |
A numeric value specifying the lower bound for the confidence interval. |
ub |
A numeric value specifying the upper bound for the confidence interval. |
Value
A list with two elements: dens (a density estimate of the bootstrap sample statistics) and stats (a list of summary statistics including number of resamples, mode, median, mean, standard deviation, lower confidence interval (lCI), and upper confidence interval (uCI)).
Regular Bootstrap with Summary Statistics
Description
Performs a regular bootstrap to generate a distribution of sample statistics and computes a set of summary statistics: mode, median, mean, standard deviation, and lower and upper confidence intervals.
Usage
reg_bootstrap(
data,
n_bootstraps = 10000,
anon = function(x) (mean(x)),
lb = 0.025,
ub = 0.975,
density_args
)
Arguments
data |
A numeric vector of data points. |
n_bootstraps |
An integer indicating the number of bootstrap samples to generate. Default is 10000. |
anon |
A function to compute the sample statistic for each bootstrap sample. Default is the mean function. |
lb |
Lower bound for the confidence interval. Default is 0.025. |
ub |
Upper bound for the confidence interval. Default is 0.975. |
density_args |
Additional arguments to be passed to |
Value
A list with two elements:
dens: a density estimate of the bootstrap sample statistics,
stats: a list of summary statistics including number of resamples, mode, median, mean, standard deviation, lower confidence interval (lCI), and upper confidence interval (uCI).
See Also
Examples
set.seed(123)
data <- rnorm(5)
result <- reg_bootstrap(data)
result$stats
Summary Method for 'extboot' Class
Description
Creates a summary table of the summary statistics computed in the
exact_bootstrap function.
Usage
## S3 method for class 'extboot'
summary(object, ...)
Arguments
object |
An object of class 'extboot', usually the output of the |
... |
Additional parameters (currently ignored). |
Value
A data.frame containing the summary statistics.
See Also
Examples
set.seed(123)
data <- rnorm(5)
result <- exact_bootstrap(data)
summary(result)
Summary Method for 'regboot' Class
Description
Creates a summary table of the summary statistics computed in the
reg_bootstrap function.
Usage
## S3 method for class 'regboot'
summary(object, ...)
Arguments
object |
An object of class 'regboot', usually the output of the |
... |
Additional parameters (currently ignored). |
Value
A data.frame containing the summary statistics.
See Also
Examples
set.seed(123)
data <- rnorm(5)
result <- reg_bootstrap(data)
summary(result)
Generate a Summary Table for Bootstrap Objects
Description
This function takes a bootstrap object and generates a summary table containing the method used and the computed summary statistics.
Usage
xboot_summary(object)
Arguments
object |
A bootstrap object of class 'extboot', 'ecboot' or 'regboot'. |
Value
A data frame containing the summary statistics with the method as the first column.