Bootstrap Inference Flashcards
How does the wild bootstrap method differ from the pairs bootstrap method, and in what situations would you use one over the other?
The pairs bootstrap resamples rows (y,x) of our data to generate bootstrap samples. The wild bootstrap transforms residuals. The wild bootstrap works better when we have a lot of extreme values in the
data as it includes all observations exactly once. The pairs bootstrap can generate samples that either exclude or include multiple copies of extreme observations
What is bootstrap inference, and how does it differ from asymptotic inference methods?
Bootstrap inference involves specifying a bootstrap DGP to construct multiple bootstrap samples. These samples are then used to calculate bootstrap test-statistics. We then use the empirical distribution of the bootstrap test-statistics to calculate a P-value, this is in contrast to asymptotic inference where we use a known statistical distribution (t, normal, etc.) to calculate a P-value.
In what types of situations is the bootstrap method particularly useful?
Bootstraps are helpful when we either don’t know what the asymptotic distribution of a statistic is, or we are in a setting where the asymptotic requirements are not satisfied. We saw the later part in class,
where the cluster robust variance estimator needs a large number of clusters for the t(G-1) distribution to have the proper test size.
How do we calculate the standard error of a sample statistic, and why is it important in statistical inference?
Various sample statistics have different standard errors, for instance for a proportion it is. We want to calculate these to take into account the variability of a sample statistic when conducting a hypothesis test
What is a p-value, and how do we interpret it in the context of hypothesis testing?
A p-value is the probability, given the null is true, of observing a statistic which is as extreme, or more extreme, then the observed value.
