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Jul 27, 2023 at 15:40 comment added Frank Harrell Yes there's undoubtedly better terminology than nonparametric. I should have left it at "we don't have a nonparametric test of means". A test that assumes symmetry would not quite qualify as nonparametric in this setting. On a slightly related matter empirical likelihood and bootstrap do not work well for means with highly skewed distributions.
Jul 27, 2023 at 14:52 comment added whuber I agree with the intuition that means are in some sense "parametric," but this term doesn't feel quite right. There are nonparametric tests for means. For instance, consider the family of all symmetric distributions of finite mean and apply any nonparametric test of medians (which coincide with their means). Although "symmetric" is the kind of strong condition we feel is needed to test means, it's still nonparametric.
Jul 27, 2023 at 14:05 history edited Frank Harrell CC BY-SA 4.0
Added info on conditional logistic regression
Jul 27, 2023 at 11:51 history answered Frank Harrell CC BY-SA 4.0