Lecture 7

Question 1

What are Computer Intensive Techniques (resampling/CIT)?

Answer 1

use of computers to compute thousands of new samples, divergent statistics or other values of interest to analyze and to validate models.

Question 2

What is a Parametric assumption?

Answer 2

based on assumptions regarding the population and the parameter of interest. A normal distribution is expected. If the expectations are not achieved, we switch to non-parametric statistics.

Question 3

What is a non-parametric assumption?

Answer 3

tests make no strong assumptions about the population, sometimes called “distribution free”.

Question 4

What are the 3 types of CIT?

Answer 4

1. Bootstrap sampling distributions and confidence intervals.
2. Monte Carlo methods.
3. Randomization tests, permutation tests, exact tests.

Question 5

Are CIT approaches essentially parametric or non-parametric?

Answer 5

Non-parametric.

Question 6

What is Bootstrapping?

Answer 6

It is “resampling with replacement” from one sample with size n.

Question 7

What can we do after Bootstrapping?

Answer 7

Compute any statistic (mean, median, standard dev. etc.) and store this value. This process is repeated 1000 times.

Question 8

What can we do after computing the statistics (Bootstrapping)?

Answer 8

With the results, a distribution is constructed, and this is compared to the initial statistic drawn from the original sample. Statistical signigicance of the original is being established.

Question 9

What are 4 advantages of Bootstrapping?

Answer 9

1. Simple test, especially with a small sample size.
2. It allows simulating the sampling distribution of many different statistics.
3. Useful when the variables are not normally distributed.
4. Useful when the relationship between variables is not linear.

Question 10

What are 2 disadvantages of Bootstrapping?

Answer 10

1. The new sampling distribution of the mean is NOT equal to the real sampling distribution of the mean.
2. The sample must be representative for the population.

Question 11

What is the Monte Carlo method?

Answer 11

Method to calculate the area of (usually) more complex areas.

Question 12

How does the Monte Carlo method work?

Answer 12

Randomly throw 1000 arrows in a known area positioned around the area you want to calculate. The chance of being “hit” is the same for every spot. if 50% of the arrows hit the area you want to calculate, you know that the surface area is 50% of the known area.

Question 13

What are 4 advantages/characteristics of the Monte Carlo method?

Answer 13

1. It can solve problems that have a probabilistic interpretation.
2. When the data set does not meet the requirements for parametric or asymptotic methods, MC can be used.
3. It involves repeatedly sampling in order to obtain a good estimate or approximation of the exact p-value.
4. Computing an exact p-value is possible via exact tests and randomization tests, but only for small data sets.

Question 14

What is the order for statistical testing (MC method)? (7 steps)

Answer 14

1. State null hypothesis and alternative hypothesis.
2. State significance level: alpha.
3. Compute degrees of freedom.
4. Compute decision rule, critical region, critical values.
5. Compute test statistic and confidence interval.
6. State the results.
7. State the conclusion.

Question 15

What is given in asymptotic methods?

Answer 15

A sufficient sample size.

Question 16

What is the one-sample T-test formula?

Answer 16

t = (Sample mean - Proposed constant for the population mean) / (Sample standard deviation / squared root of sample size)

Question 17

What is the Z-test formula?

Answer 17

Z = (Sample mean - population mean) / (population standard deviation / squared root of sample size)