Bootstrapping

Question 1

What is the “original sample”?

Answer 1

The initial sample from some given distribution from which you will create bootstrap samples

Question 2

How do we form bootstrap samples?

Answer 2

We select an observation from the original sample, record it, return it to the sample and repeat the earlier steps until we have recorded a number of observation which is equal to the size of the original sample

Question 3

May we have repetition of observations within a single bootstrap sample?

Answer 3

Yes

Question 4

What “data structure” do we often use to store bootstrap samples in R?

Answer 4

An Mxn matrix where m represents the number of rows (i.e.number of bootstrap samples) and n represents the sample size.

As well as an Mx1 matrix (i.e. vector) to store our statistic of interest (eg. bootstrap sample means)

Question 5

What is the Bootstrap Assumption?

Answer 5

The bootstrap samples relate to the original sample in a similar way to how the original sample relates to the population of interest. The sampling error between the 3 groups respective will be equal.

x(b) - x(o) ~ x(o) - mu

Question 6

What is sampling error?

Answer 6

The difference between the original sample mean and the population of interest mean (i.e. mu)

= x(o) - mu

Question 7

What is bootstrap sampling error?

Answer 7

The difference between the bootstrap sample mean and the original sample mean

= x(b) - x(o)