This post discusses the need for smoothed version of the statistical bootstrap. I start with a negative result of the standard bootstrap, and introduce smoothing as a practical, and necessary improvement.
Suppose you have 100 unique values and you draw a new sample of 100 observations with replacement. How many unique values would you expect to see in this new sample?
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On average, fewer than 70 of the original values would appear. Unfortunately, you are deprived of using more than 30% of your data, and that is hard to remedy.
Why does ~30% of your data end up being left out of each sample?