A Comment on: "Invidious Comparisons: Ranking and Selection as Compound Decisions" by Jiaying Gu and Roger Koenker.

Suppose, for example, that for each I i i , we observe HT <math altimg="urn:x-wiley:00129682:media:ecta200494:ecta200494-math-0018" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi><mn>1</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">...</mi><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi><mi>T</mi></mrow></msub><mover accent="true"><mo>~</mo><mrow><mi mathvariant="normal">iid</mi></mrow></mover><msub><mrow><mi>F</mi></mrow><mrow><msub><mrow><mi> </mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub></math> ht , for some parametric family of distributions HT <math altimg="urn:x-wiley:00129682:media:ecta200494:ecta200494-math-0019" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>F</mi></mrow><mrow><mi> </mi></mrow></msub></math> ht . Assume independence between units I i i , and let HT <math altimg="urn:x-wiley:00129682:media:ecta200494:ecta200494-math-0020" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>y</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mover accent="true"><mi> </mi><mo> </mo></mover></mrow><mrow><mi>i</mi></mrow></msub></math> ht be the maximum likelihood estimator based on HT <math altimg="urn:x-wiley:00129682:media:ecta200494:ecta200494-math-0021" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi><mn>1</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">...</mi><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi><mi>T</mi></mrow></msub></math> ht . Asymptotic Approximations Gu and Koenker regard the normality assumption on HT <math altimg="urn:x-wiley:00129682:media:ecta200494:ecta200494-math-0017" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>y</mi></mrow><mrow><mi>i</mi></mrow></msub></math> ht as an approximation. [Extracted from the article]