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Pairwise-comparison estimation with nonparametric controls. (2013). Jochmans, Koen.
In: Sciences Po Economics Discussion Papers.
RePEc:spo:wpecon:info:hdl:2441/dambferfb7dfprc9m01h6f4h2.

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  1. Informational Content of Factor Structures in Simultaneous Binary Response Models. (2022). Maurel, Arnaud ; Zhang, Yichong ; Khan, Shakeeb.
    In: Papers.
    RePEc:arx:papers:1910.01318.

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  2. Informational Content of Factor Structures in Simultaneous Binary Response Models. (2020). Maurel, Arnaud ; Zhang, Yichong ; Khan, Shakeeb.
    In: IZA Discussion Papers.
    RePEc:iza:izadps:dp14008.

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  3. Informational Content of Factor Structures in Simultaneous Binary Response Models. (2019). Maurel, Arnaud ; Zhang, Yichong ; Khan, Shakeeb.
    In: Boston College Working Papers in Economics.
    RePEc:boc:bocoec:985.

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  4. Multiplicative-error models with sample selection. (2015). Jochmans, Koen.
    In: Journal of Econometrics.
    RePEc:eee:econom:v:184:y:2015:i:2:p:315-327.

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  5. Identification in Bivariate binary-choice Models with elliptical innovations. (2011). Jochmans, Koen.
    In: Sciences Po publications.
    RePEc:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09ij4oogc0g.

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References

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  4. Apply Theorem 3 in Sherman (1994a) with, using Sherman’s notation, ⇥n = ⇥, n = 1, and any ↵ 2 (0, 1) to get En[rn(, ; b, ✓)] = Op ⇣ 1 d(⌅) k n ⌘
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  5. Aradillas-Lopez, A., B. E. Honore, and J. L. Powell (2007). Pairwise difference estimation with nonparametric control variables. International Economic Review 48, 1119–1158.

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  11. 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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  12. First, combine the Euclidean properties of the class Q with Corollary 17 and Corollary 21 in Nolan and Pollard (1987) to see that the class { d(⌅) k rn(, ; , ✓) : 2 , ✓ 2 ⇥} is Euclidean for an envelope whose second moment under P exists; denote its bound by R. Further observe that rn(, ; , ✓) is P-degenerate on D ⌦ D and that rn(, ; , ✓0) = 0.
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  24. Pairwise-comparison estimation 25 Ichimura, H. and S. Lee (2010). Characterization of the asymptotic distribution of semiparametric M-estimators. Journal of Econometrics 159, 252–266.

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  30. uniformly over Op(1/ q d(⌅) k n) = Op(1) neighborhoods of ✓0. The p n-consistency of b✓ then follows from another application of Theorem 1 of Sherman (1994a).
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