Hence, EX          1 ∑ k′̸=k |Ik′| ∑ k′̸=k ∑ i∈Ik′ /BD Ai=a∆2iWi       2 ∞    =Op ( sγ log(d) log(p) nN ) =op ( log(p) n ) , since sγ log(d) = o(N)

≤ 2EX ⏐ ⏐ ⏐ ⏐ ⏐[Y (1) −µ∗ 1(X)] [ A ˆπ(−k,−k′)(X) − A π∗(X) ] ⏐ ⏐ ⏐ ⏐ ⏐ 2 + 2EX ⏐ ⏐ ⏐ ⏐ ⏐[Y (0) −µ∗ 0(X)] [ 1 −A 1 − ˆπ(−k,−k′)(X) − 1 −A 1 −π∗(X) ] ⏐ ⏐ ⏐ ⏐ ⏐ 2 ≤ 2 √ EX|A [Y (1) −

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Semi-supervised inference for treatment heterogeneity

stat.ME · 2025-09-05 · conditional · novelty 6.0

Semi-supervised estimators for total and explained treatment heterogeneity, with an optimally weighted procedure that is guaranteed to be at least as efficient as supervised estimation.

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Semi-supervised inference for treatment heterogeneity stat.ME · 2025-09-05 · conditional · none · ref 8
Semi-supervised estimators for total and explained treatment heterogeneity, with an optimally weighted procedure that is guaranteed to be at least as efficient as supervised estimation.

Hence, EX          1 ∑ k′̸=k |Ik′| ∑ k′̸=k ∑ i∈Ik′ /BD Ai=a∆2iWi       2 ∞    =Op ( sγ log(d) log(p) nN ) =op ( log(p) n ) , since sγ log(d) = o(N)

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