12 Questions
What is the difference between the empirical bootstrap and the parametric bootstrap?
The empirical bootstrap makes no assumptions about the underlying distribution and draws bootstrap samples by resampling the data, while the parametric bootstrap generates the bootstrap sample from a parametrized distribution.
What are the elements of using the parametric bootstrap to estimate a confidence interval for a parameter?
The elements include drawing data from a distribution with an unknown parameter, estimating the parameter, and drawing bootstrap samples from the estimated distribution.
How is the mean used in the bootstrap process?
The mean is used instead of the median in the bootstrap process.
What is the principle behind using the distribution of bootstrap differences?
The bootstrap principle states that the distribution of bootstrap differences can be used as an approximation for the original distribution.
What is the sample mean in the toy example?
40.3
What does the 80% bootstrap confidence interval aim to estimate?
The mean µ of the underlying distribution.
What critical values are needed to find the 80% confidence interval?
δ.1 and δ.9
Explain the significance of the 80% confidence interval [x - δ.1 , x - δ.9].
It provides an 80% confidence interval for the true mean µ.
What is the purpose of sorting the list of numbers from smallest to biggest?
To find the smallest and largest values in the data set
What is the 80% bootstrap confidence interval for the parameter µ in this example?
[38.7, 41.7]
Why is generating 10000 or more bootstrap samples recommended when using R?
To obtain a very accurate estimate of δ.∗1 and δ.∗9
What is the justification for the use of the bootstrap principle?
Resampling gives a decent estimate of how the point estimate might vary
Test your knowledge of sorting numerical data from smallest to largest. Practice arranging a given set of numbers in ascending order.
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