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We derive a necessary and sufficient condition under which noisy estimates are informative about extreme quantiles, along with sufficient rate and moment conditions. Under these conditions, we establish an extreme value theorem and an intermediate order theorem for noisy estimates. These results yield simple optimization-free confidence intervals (CIs) for extreme quantiles. Simulations show that our CIs have favorable coverage and that the rate conditions matter for the validity of inference. We illustrate the method with an application to firm productivity differences across areas of varying population density. By analyzing the left tails of the productivity distributions, we find no evidence of stronger firm selection in more densely populated areas.<\/jats:p>","DOI":"10.1017\/s0266466625100315","type":"journal-article","created":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T06:42:16Z","timestamp":1769755336000},"page":"1-52","source":"Crossref","is-referenced-by-count":0,"title":["INFERENCE ON EXTREME QUANTILES OF UNOBSERVED INDIVIDUAL HETEROGENEITY"],"prefix":"10.1017","author":[{"given":"Vladislav","family":"Morozov","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041nas322","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e4t Bonn"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,1,30]]},"reference":[{"key":"S0266466625100315_r6","article-title":"Skill, scale and value creation in the mutual fund industry","author":"Barras","year":"2021","journal-title":"The Journal of 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