How can bootstrapping with replacement improve your understanding of the variance of a population over that of the sample itself? If you subsample from your sample with the same values allowed to be selected more than once, it seems even less representative of the variance of a population than the original sample, given that you may draw a subsample that are all one value. In the ISLR text, they show how the estimated population variance of a certain measure can be improved through subsampling a sample with replacement. Is there some intuition or theorems that could help me to understand why this method is an effective means of improving the estimated variance of a population?


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