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I thought I'd ask a fairly fundamental question regarding confidence intervals at the risk of potentially furious backlash from the stats.stackexchange community.

However, I've never quite yet found a satisfying answer for it. In particular, I've never quite found a satisfying explanation on the `repeated sampling' assumption of a confidence interval in the context of a finite data sample.

Therefore, could someone explain how the repeated sampling takes place with a confidence interval? Is it a theoretical assumption based on an assumed infinite underlying data generating process, or is there some genuine repeated sampling that takes place, procedurally?

I know this is a controversial topic. But I would love to hear some genuine feedback. Response to reference request, Definition 1, here: https://link.springer.com/article/10.3758/s13423-015-0947-8

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EB3112
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  • Do you mean resampling? Yes you can construct confidence intervals through resampling, see bootstrap confidence intervals – Ggjj11 Nov 23 '23 at 19:48
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    I think that you need to fill us in on what you mean by "the 'repeated sampling' assumption". Do you mean the underlying frequentist model of probability, or something about confidence intervals in the setting of sequential sampling? – Michael Lew Nov 23 '23 at 19:50
  • Could you supply a reference to your statement that confidence intervals are controversial? That might help us understand what you're trying to get at. Have you found (among other relevant threads about CIs here on CV) https://stats.stackexchange.com/questions/6652/what-precisely-is-a-confidence-interval? And, perhaps, tell us why you would expect a "backlash" arising from any clear, reasonably researched on-topic question? – whuber Nov 23 '23 at 19:50
  • Hi @whuber. Regarding a reference on CI's being 'controversial.' This comes from some talks I've been watching regarding the foundations of frequentism, such as here: https://www.youtube.com/watch?v=eDMGDhyDxuY&t=2227s. Regarding the 'backlash,' I guess I know that many people are better informed on matters than I am. – EB3112 Nov 23 '23 at 19:56
  • Hi @MichaelLew. I guess this is the essence of my question. What precisely is meant by repeated sampling when in reality we have a finite sample from an otherwise often infinite data generating process – EB3112 Nov 23 '23 at 20:13
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    I think you need to follow the suggestion to look at other CI questions on this site. A quick comment to set you on the path. There is no repeated sampling 'assumption'. An implication of the assumption of random sampling from the assumed statistical model is that: "IF we were to repeatedly sample then .........." Now what ........ is is based on the weak law of large numbers. Note: No repetitions are actually required. So no concern about needing an infinite number of repetitions. – Graham Bornholt Nov 23 '23 at 21:39
  • Hi @GrahamBornholt. Thanks. I get what you're saying. It's very much an if-then statement – EB3112 Nov 23 '23 at 23:11
  • One way to read the quotation is to understand "... in repeated sampling ..." as a shorthand for a probability model for the data and its application prior to obtaining the sample (that is, it includes the idea that the probability is not conditioned on the data). – whuber Nov 24 '23 at 15:03
  • Thanks @whuber. Got you. Thanks – EB3112 Nov 24 '23 at 17:24

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