Week 4 - Bootstrap

Question 1

General format for CIs

Answer 1

estimate ± quantile × se(estimate)

If we know the quantiles -> we can calculate a CI
Using CLT or knowing sampling distribution

However, Bootstrap is an alternative method if we can’t use CLT

Question 2

Bootstrap

Answer 2

• Create new datasets (bootstrap samples) by randomly picking data points from the original dataset, allowing the same point to be picked more than once (with replacement)
• Each new dataset will have the same size as the original one
• Repeat this process many times to get approximate sampling distribution
• We can this bootstrapping to understand uncertainty of estimate and calculate CI

Question 3

If sample size is not the same as original

Answer 3

Lead to unreliable and biased estimates

• small sample size -> large variability (bigger CI)
• large sample size -> small variability (tight CI) (not accurate)

Question 4

Why use bootstrap?

Answer 4

Bootstrap uses all of data and thus is more versatile if we have non-normal data

• When we have smaller dataset
• Non-normal distribution
• can be applied to any point estimator
• Can incorporate skewness

Question 5

Difference between simulation and bootstrap

Answer 5

Simulation starts with an assumed or known model (e.g., normal distribution, Poisson process) to generate data

While bootstrap relies on the original dataset as the only “population” available