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To clarify, bootstrapping is the same thing as sampling from the ECDF because the ECDF is a step function, which implies that there are only discrete number of values that have positive probabilit?

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Sampling from ECDF would give you same kind of samples as sampling randomly with replacement from the data, but bootstrap is not only about sampling, but it is the whole statistical procedure to estimating uncertainties. Moreover, bootstrap also defines the rules of sampling, e.g. that you take $n$ out of $n$ samples with replacement. There are also other variants of bootstrap then the vanilla one, where the procedures differ, like stratified bootstrap, or parametric bootstrap. So they’re not “the same”.

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  • $\begingroup$ ok so when professor says bootstrapping is same as sampling from ECDF, it only applies to vanilla empirical, nonparametric bootstrapping. $\endgroup$ May 17, 2020 at 8:03
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    $\begingroup$ @MinYoungKim and only the sampling part, not the whole procedure $\endgroup$
    – Tim
    May 17, 2020 at 8:10

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