How to Calculate a Bootstrap Standard Error in R

Bootstrap Standard Error in R, Bootstrapping is a technique for calculating the standard error of a mean.

The following is the basic procedure for calculating a bootstrapped standard error.

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From a given dataset, take k repeated samples using replacement and calculate the standard error for each sample: s/√n

As a result, there are k distinct standard error estimates. Take the mean of the k standard errors to get the bootstrapped standard error.

The following examples show how to calculate a bootstrapped standard error in R using two distinct methods.

Approach 1: Boot Package

The boot() function from the boot library is one technique to calculate a bootstrap standard error in R.

In R, the following code demonstrates how to compute a bootstrap standard error for a given dataset.

Let’s take the example reproducible

set.seed(123)

Now load the boot library

library(boot)

We can define the dataset

x <- c(112, 64, 84, 78, 67, 221, 125, 219, 45, 79)

Let’s create a function to calculate mean

meanF <- function(x,i){mean(x[i])}

Okay, now we can calculate standard error using 500 bootstrapped samples

boot(x, meanF, 5000)
ORDINARY NONPARAMETRIC BOOTSTRAP
Call:
boot(data = x, statistic = meanF, R = 5000)
Bootstrap Statistics :
    original   bias    std. error
t1*    109.4 -0.13972    18.41172

The “original” number of 109.4 represents the dataset’s mean. The bootstrap standard error of the mean is represented by the value 18.41 in the “std. error” column.

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In this example, we used 5000 bootstrapped samples to estimate the standard error of the mean, but we could have used 1,000, 10,000, or any other number of bootstrapped samples.

Approach 2: Own Formula

We can also construct our own code to calculate a bootstrapped standard error.

The code below demonstrates how to do so:

create a repeatable example

set.seed(123)

Let’s load the boot library

library(boot)

Now we can use the same dataset

x <- c(112, 64, 84, 78, 67, 221, 125, 219, 45, 79)
mean(replicate(500, sd(sample(x, replace=T))/sqrt(length(x))))
[1] 18.11736

18.11 is the bootstrapped standard error. This standard error looks a lot like the one determined in the previous example.

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