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Nonparametric Inference on Quantile Marginal Effects. (2014). Kaplan, David.
In: Working Papers.
RePEc:umc:wpaper:1413.

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  1. Fractional order statistic approximation for nonparametric conditional quantile inference. (2017). Kaplan, David ; Goldman, Matt.
    In: Journal of Econometrics.
    RePEc:eee:econom:v:196:y:2017:i:2:p:331-346.

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  2. Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics. (2016). Kaplan, David ; Goldman, Matt.
    In: Working Papers.
    RePEc:umc:wpaper:1620.

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  3. Fractional order statistic approximation for nonparametric conditional quantile inference. (2016). Kaplan, David ; Goldman, Matt.
    In: Papers.
    RePEc:arx:papers:1609.09035.

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  4. Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics. (2015). Kaplan, David ; Goldman, Matt.
    In: Working Papers.
    RePEc:umc:wpaper:1503.

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  5. Fractional order statistic approximation for nonparametric conditional quantile inference. (2015). Kaplan, David ; Goldman, Matt.
    In: Working Papers.
    RePEc:umc:wpaper:1502.

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References

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  11. Goldman, M. and Kaplan, D. M. (2014a). Fractional order statistic approximation for nonparametric conditional quantile inference. Working paper, available at http://web. missouri.edu/~kaplandm/personalResearch.html.

  12. Goldman, M. and Kaplan, D. M. (2014b). Nonparametric inference on conditional quantile treatment effects and other objects using L-statistics. Working paper, available at http: //web.missouri.edu/~kaplandm/personalResearch.html.

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  22. Sasaki, Y. (2012). What do quantile regressions identify for general structural functions? Working paper, available at http://www.econ2.jhu.edu/People/Sasaki. A Mathematical proofs Lemma 1 proof For the approximation error, consider a general scalar function f() where f00 () is Lipschitz continuous. For small h > 0, Taylor approximation yields f(x0 + h) = f(x0) + hf0 (x0) + (1/2)h2 f00 (˜ x), (12) f(x0 − h) = f(x0) − hf0 (x0) + (1/2)h2 f00 ( x), (13) where x0 − h ≤ x ≤ x0 ≤ ˜ x ≤ x0 + h. Subtracting (13) from (12) and dividing by 2h yields f(x0 + h) − f(x0 − h) 2h = f0 (x0) + (1/2)h2 [f00 (˜ x) − f00 ( x)]/(2h) = f0 (x0) + O(h2 ) (14) since the Lipschitz continuity implies |f00 (˜ x) − f00 (

  23. The endpoints from either method we use are asymptotically (first-order) equivalent to those from derived from asymptotic normality of a sample quantile, so the PDF is proportional to h √ Nn (Chaudhuri, 1991). Multiplying the bias from Lemma 1 by h √ Nn yields a CPE contribution of O(h3 √ Nn) from bias. The original proof showed an o(h3 ) remainder with an extra derivative and o(h2 ) when weakening the Lipschitz continuity in our A2 and A3 to H older continuity with any exponent γ > 0; the O(h3 ) remainder when γ = 1 is readily seen from the original derivation.
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