Timeline for Are bootstrapped samples considered to be coming from the same distribution as the original sample?
Current License: CC BY-SA 4.0
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| Nov 16, 2023 at 17:39 | comment | added | EngrStudent | I said it. :) In general, for continuous distributions, the “true” distribution has infinite number of values in the domain. It is rare to get a summary statistic on sampled data that matches the analytic result to round off. More rare two get two fundamentally different statistics matching to round off. Many samples reduce the error but not all the way to zero. Mean is fun but 12th centered moment is harder. | |
| Nov 16, 2023 at 17:01 | comment | added | Dave | @EngrStudent Who said anything about "in the limit of many samples"? | |
| Nov 16, 2023 at 16:59 | comment | added | EngrStudent | Finite samples is, impo, nearly the opposite of “in the limit of many samples”. 50 < 20k < infinity | |
| Nov 16, 2023 at 16:42 | history | edited | Dave | CC BY-SA 4.0 |
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| Nov 16, 2023 at 16:35 | comment | added | Dave |
@ShamisenExpert Isn't that $\mathcal{D}$ on slide ten the empirical distribution and not the original distribution? I think that $\mathcal{D}$ is what I call x.
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| Nov 16, 2023 at 16:34 | history | edited | Dave | CC BY-SA 4.0 |
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| Nov 16, 2023 at 16:34 | comment | added | Shamisen Expert | Thank you Dave. This makes me more confused actually. Became I am looking at this in the context of bias and variance trade off. See page 10/23 by a Professor at Cornell which says the bootstrapped samples D_k has the same distribution as the original one. people.orie.cornell.edu/mru8/orie4741/lectures/… | |
| Nov 16, 2023 at 16:29 | history | answered | Dave | CC BY-SA 4.0 |