how to do bootstrap to get variances in r

To estimate the variance of a statistic (such as the mean or the standard deviation) using the bootstrap method in R, we can follow these steps:

1. Define a function that calculates the statistic of interest based on a sample of data. Let's call it my_stat.

main.r
# Example function
my_stat <- function(data) {
  # Calculate the variance of the data
  var(data)
}
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2. Generate a large number of resamples of the data by sampling with replacement from the original data set. We can use the boot function from the boot package to do this. The R argument specifies the number of resamples to generate.

main.r
# Example data
data <- rnorm(100)

# Generate resamples
library(boot)
resamples <- boot(data, my_stat, R = 1000)
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3. Calculate the variance of the resampled statistic. The boot function returns a list with several elements, including the bootstrap estimates of the statistic (t) and its variance (t0).

main.r
# Calculate variance of bootstrap estimates
boot_var <- var(resamples$t)

# Calculate the standard error of the bootstrap estimate
boot_se <- sqrt(boot_var)

# Print the results
cat("Bootstrap variance:", boot_var, "\n")
cat("Standard error of bootstrap estimate:", boot_se, "\n")
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By repeating this procedure many times, we obtain a good estimate of the variance of the statistic, which is often more robust than the theoretical or asymptotic formulae.