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Mar 29, 2022 at 11:33 comment added Iosif Pinelis @π314 : yes, it seems so for large $m$, at least if the distribution is atomless.
Mar 29, 2022 at 6:03 comment added π314 Eg, if $m \rightarrow \infty$ then I'd think the estimate converges to the correct value, no?
Mar 29, 2022 at 5:47 comment added π314 Thanks @Iosif Pinelis for pointing this out! I think my next step will be to try to understand if there are any "niceness" conditions on the distribution and or condition on the relationship between $m$ and $n$ that would suffice to imply that the estimator is approximately correct. If you have any intuition on this, I'd love to hear!
Mar 29, 2022 at 5:44 vote accept π314
Mar 28, 2022 at 20:24 history edited Iosif Pinelis CC BY-SA 4.0
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Mar 28, 2022 at 20:14 history answered Iosif Pinelis CC BY-SA 4.0