How does the Bootstrap method work?

Bhawna G. Panwar

1 minute read

Question of the day?

Suppose we have a normal population with a mean of 3 and a standard deviation of 1, how would we illustrate the bootstrap method here?

set.seed(1)
srs <- rnorm(25, mean=3)
resamps <- replicate(1000, sample(srs, 25, TRUE), simplify = FALSE)
x_bar_star <- sapply(resamps, mean, simplify =TRUE)

Let’s create a histogram here and fit normal curve.

hist(x_bar_star, breaks = 40, prob = TRUE)
curve(dnorm(x, 3, 0.2), add = TRUE)

We can calculate the difference now.

mean(x_bar_star)
## [1] 3.167102
mean(srs)
## [1] 3.168665
mean(x_bar_star) - mean(srs)
## [1] -0.001562762

Now we observe the standard error of the mean x_bar_star with the sample standard deviation of the resample statistics.

sd(x_bar_star)
## [1] 0.1826719
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