Invidious Comparisons: Ranking and Selection as Compound Decisions

Gu, Jiaying; Koenker, Roger

doi:10.3982/ecta19304

Cited by 11 publications

(9 citation statements)

References 61 publications

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“…In the setting of Gu and Koenker (2021), the features of interest

θ_{i}

are, of course, unknown, but it is assumed that, for each population, repeated measurements of the underlying

θ_{i}

are observed. More precisely, the observed measurements are given by

Y_{i, t} = θ_{i} + σ_{i} ϵ_{i, t}

with

ϵ_{i, t}, i = 1, normal…, n

t = 1, normal…, T_{i}

i.i.d.…”

Section: Overview Of Gu and Koenker (2021)mentioning

confidence: 99%

“…For the purposes of our discussion, it is convenient to assume τ 2 = 0. As noted by Gu and Koenker (2021), when this is the case, for a suitably chosen value of τ 1 , the problem is closely related to testing the family of null hypotheses…”

Section: Overview Of Gu and Koenker (2021)mentioning

confidence: 99%

“…For the purposes of our discussion, it is convenient to assume

τ_{2} = 0

. As noted by Gu and Koenker (2021), when this is the case, for a suitably chosen value of

τ_{1}

, the problem is closely related to testing the family of null hypotheses

H_{i} : θ_{i} \geq θ_{α} versus K_{i} : θ_{i} < θ_{α}

in a suitable way. In particular, for an appropriately chosen value of

τ_{1}

, the problem is equivalent to testing this family of null hypotheses so as to minimize false non‐discoveries as measured by the quantity

E false[\sum_{1 \leq i \leq n} I false{θ_{i} \geq θ_{α} false} false(1 - δ_{i} false) false]

subject to controlling the marginal false discovery rate, meaning

mFDR \leq γ

, where

mFDR = \frac{\sum_{1 \leq i \leq n} E [I {θ_{i} < θ_{α}} δ_{i}]}{\sum_{1 \leq i \leq n} E [δ_{i}]} .

As shown by Genovese and Wasserman (2002), in the asymptotic framework considered by Gu and Koenker, in which n tends to infinity, the marginal false discovery rate is approximately equal to the more familiar false discovery rate, denoted by FDR and defined to be

FDR = E [true \sum_{...}

…”

Section: Overview Of Gu and Koenker (2021)mentioning

confidence: 99%

“…1 Then the family selects all CZs that are outside of this confidence set. Second, it ranks CZs by their posterior tail probability as in Gu and Koenker (2021) using only the FDR constraint (

τ_{2} = 0

α = 0.1

, and some value for γ 2 . Table I shows the CZs selected by the two procedures, denoted by “MRSW” and “GK,” for different values of γ .…”

Section: Empirical Illustrationmentioning

confidence: 99%

See 3 more Smart Citations

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

Mogstad

Romano

Shaikh

et al. 2023

ECTA

View full text Add to dashboard Cite

“…In the setting of Gu and Koenker (2021), the features of interest

θ_{i}

are, of course, unknown, but it is assumed that, for each population, repeated measurements of the underlying

θ_{i}

are observed. More precisely, the observed measurements are given by

Y_{i, t} = θ_{i} + σ_{i} ϵ_{i, t}

with

ϵ_{i, t}, i = 1, normal…, n

t = 1, normal…, T_{i}

i.i.d.…”

Section: Overview Of Gu and Koenker (2021)mentioning

confidence: 99%

Section: Overview Of Gu and Koenker (2021)mentioning

confidence: 99%

“…For the purposes of our discussion, it is convenient to assume

τ_{2} = 0

. As noted by Gu and Koenker (2021), when this is the case, for a suitably chosen value of

τ_{1}

, the problem is closely related to testing the family of null hypotheses

H_{i} : θ_{i} \geq θ_{α} versus K_{i} : θ_{i} < θ_{α}

in a suitable way. In particular, for an appropriately chosen value of

τ_{1}

, the problem is equivalent to testing this family of null hypotheses so as to minimize false non‐discoveries as measured by the quantity

E false[\sum_{1 \leq i \leq n} I false{θ_{i} \geq θ_{α} false} false(1 - δ_{i} false) false]

subject to controlling the marginal false discovery rate, meaning

mFDR \leq γ

, where

mFDR = \frac{\sum_{1 \leq i \leq n} E [I {θ_{i} < θ_{α}} δ_{i}]}{\sum_{1 \leq i \leq n} E [δ_{i}]} .

FDR = E [true \sum_{...}

…”

Section: Overview Of Gu and Koenker (2021)mentioning

confidence: 99%

“…1 Then the family selects all CZs that are outside of this confidence set. Second, it ranks CZs by their posterior tail probability as in Gu and Koenker (2021) using only the FDR constraint (

τ_{2} = 0

α = 0.1

, and some value for γ 2 . Table I shows the CZs selected by the two procedures, denoted by “MRSW” and “GK,” for different values of γ .…”

Section: Empirical Illustrationmentioning

confidence: 99%

See 2 more Smart Citations

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

Mogstad

Romano

Shaikh

et al. 2023

ECTA

View full text Add to dashboard Cite

“… Gu and Koenker ( 2020 , henceforth GK) offer empiricists beset by the “league table mentality” a powerful suite of tools for selecting extreme performers based on noisy measurements. GK's basic insight is to reformulate tail selection as a large scale inference problem in which the selection of a unit failing to exceed some tail performance threshold constitutes a false discovery.…”

mentioning

confidence: 99%