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Koen, Jochmans. (2013) Pairwise-comparison estimation with nonparametric controls.
In: Sciences Po Economics Discussion Papers. RePEc:spo:wpecon:info:hdl:2441/dambferfb7dfprc9m01h6f4h2.
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Differentiate r✓⌧(d; 0, ✓0) = t(z)⇡(v, ⇠; 0, ✓0) with respect to ⇠0 and take expectations conditional on Z = Zi. Then r✓⇣(Wi; 0, ✓0) follows readily. Contrary to ⌃✓✓ and ⌃✓ , however, this expression does not symmetrize because of the conditioning on Z = Zi in r✓ (Zi; 0, ✓0). 2 Proof of Proposition 4.4: Apply Lemma A.1 in Carroll et al. (1997).
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