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- Title
A Comment on: "Invidious Comparisons: Ranking and Selection as Compound Decisions" by Jiaying Gu and Roger Koenker.
- Authors
Mogstad, Magne; Romano, Joseph P.; Shaikh, Azeem M.; Wilhelm, Daniel
- Abstract
In their paper, "Invidious Comparisons: Ranking and Selection as Compound Decisions", the authors, Gu and Koenker, masterfully develop an empirical Bayes approach to the problem of choosing the "best" (or, equivalently, "worst") of I n i populations indexed by HT <math altimg="urn:x-wiley:00129682:media:ecta200496:ecta200496-math-0001" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mi mathvariant="normal">...</mi><mo>,</mo><mi>n</mi></math> ht , where "best" is measured in terms of a feature of interest that is denoted by HT <math altimg="urn:x-wiley:00129682:media:ecta200496:ecta200496-math-0002" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi> </mi></mrow><mrow><mi>i</mi></mrow></msub></math> ht . Here, HT <math altimg="urn:x-wiley:00129682:media:ecta200496:ecta200496-math-0069" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi> </mi></mrow><mrow><mi>i</mi></mrow></msub></math> ht is the value-added of the I i i th teacher and "best" means being among the top I i fraction of all teachers in terms of HT <math altimg="urn:x-wiley:00129682:media:ecta200496:ecta200496-math-0070" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi> </mi></mrow><mrow><mi>i</mi></mrow></msub></math> ht . Since controlling the HT <math altimg="urn:x-wiley:00129682:media:ecta200496:ecta200496-math-0098" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi mathvariant="italic">FWER</mi></mrow><mrow><mi> </mi></mrow></msub></math> ht for all I i is more stringent than controlling the I FDR i , it is natural to expect GK to select more CZs.
- Subjects
FALSE discovery rate; MARGINAL distributions
- Publication
Econometrica, 2023, Vol 91, Issue 1, p53
- ISSN
0012-9682
- Publication type
Article
- DOI
10.3982/ECTA20460