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Can a sample size be too small to bootstrap?
Now if the sample size is very small like say 4 the bootstrap may not work just because the set of possible bootstrap samples is not rich enough. In my book or Peter Hall’s book this issue of two small a sample size is discussed.
Why do we use bootstrap instead of random subsampling?
Bootstrap methodology. Why resample “with replacement” instead of random subsampling? The bootstrap method has seen a great diffusion in the last years, I also use it a lot, especially because the reasoning behind is quite intuitive. But that’s one thing I don’t understand.
Is it a problem to find bootstrap CI for sample mean?
It is not a problem to find bootstrap CI for the sample mean. It surely will be correct. The problem is whether your tiny sample can correctly represent (describe) the population it comes from. If not, while sample mean and CI are good, they still may be far from true population mean.
What does the presence of repeated cases in bootstrap mean?
The presence of a repeated case in a particular bootstrap sample represents members of the underlying population that have characteristics close to those of that particular repeated case. Leave-one-out or leave-several-out approaches, as you suggest, can also be used but that’s cross validation rather than bootstrapping.
Which is an example of a problem with bootstrap?
(1) Issues with resampling. One of the problems with bootstrap, either for small or large samples, is the resampling step. It is not always possible to resample while keeping the structure (dependence, temporal.) of the sample. An example of this is a superposed process.
Is it OK to use D distribution in Bootstrap?
In reality the distribution is not exactly D, but it’s ok as long as the sample size is large enough. Since in this case the sample size is too small, let’s switch to the (non-parametric) bootstrap that doesn’t make any distributional assumptions. Problem solved! In my opinion, that’s not what bootstrap is for.
Are there any problems with nonparametric bootstrap?
In case you really want to find issues of using nonparametric bootstrap, here are two problems: (1) Issues with resampling. One of the problems with bootstrap, either for small or large samples, is the resampling step. It is not always possible to resample while keeping the structure (dependence, temporal.) of the sample.
Which is the sampling distribution assumed in Bootstrap?
The basic nonparametric bootstrap assumes that the sample is taken at random from a population. So for any sample size n the distribution for samples chosen at random is the sampling distribution assumed in bootstrapping.
https://www.youtube.com/watch?v=9STZ7MxkNVg