Lecture 7 - Bootstrap Part I

Question 1

What is a non-parametric simulation?

Answer 1

Sample from the data to create a new data set.

Question 2

What is a parametric simulation?

Answer 2

Simulate from a distribution based on the data to create new data sets.

Question 3

What is the percentile method?

Answer 3

• Resample the data
• Order the means (or quantity of interest)
• Lower limit is (α/2)(b+1) th value
• Upper limit is (1-α)/2(b+1)th value

Question 4

What are the pros and cons of the percentile method?

Answer 4

Pros:
Simple to apply
General and robust method of setting CIs
No need for parametric assumption about f() or quantity of interest

Cons:
Assumes observations/samples are iid
Requires a reasonably large number of samples (20-30 or more)
In complex examples, hard to see what the unit for resampling should be
Generally only asymptotically exact as b and n tend to infinity.

Question 5

What is the algorithm for parametric bootstrap?

Answer 5

Fit a parametric model f(θ) to the data.
Generate resamples by simulating from the fitted model.
Use to resamples to obtain CIs.

Question 6

What are the pros and cons of parametric bootstrapping?

Answer 6

Pros:
General and robust method of setting CIs
Observations don’t need to be iid

Cons:
Generally only asymptotically exact as b and n tend to infinity
Must assume a parametric model for f(θ)