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Asymptotic Properties of Empirical Quantile-Based Estimators

Julien Chhor, Xavier D'Haultfœuille, Jérémy L'Hour, Martin Mugnier

arXiv 30 Jun 2026 · Econometrics

arXiv:2607.00219 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We consider inference for parameters of the form $θ_0 = E[F_Y^{-1}\circ F_Z(X)]$ for some variables $X$, $Y$ and $Z$. Such parameters appear, in particular, in the “changes-in-changes” model of \cite{AtheyImbens2006}. We first establish that $\widehatθ$, a plug-in estimator of $θ_0$, is root-$n$ consistent and asymptotically normal under weaker conditions than those previously available, allowing in particular for unbounded variables. Next, we propose a new estimator of the asymptotic variance of $\widehatθ$ and show its consistency, also allowing for unbounded variables. Monte Carlo simulations suggest that the conditions for root-$n$ consistency and asymptotic normality are, in some sense, minimal. These simulations highlight that our variance estimator also leads to more accurate inference than some alternative approaches.

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16
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34
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Athey, Susan and Imbens, Guido W (2006) Identification and Inference in Nonlinear Difference-in-Differences Models0.693131100%
2Shorack, G.R. and Wellner, J.A (1986) Empirical Processes with Applications to Statistics0.5854175%
3Brendan K. Beare and Tetsuya Kaji (2026) Convergence in distribution of the P-P process in $L^1[0,1]$0.51121100%
4Csörg o, Miklos and Csorgo, Sandor and Horváth, Lajos and Mason, Dav… (1986) Weighted empirical and quantile processes0.51121100%
5de Chaisemartin, C and D’Haultfœuille, X (2018) Fuzzy Differences-in-Differences0.40511100%
6Jones, M.C (1990) VARIABLE KERNEL DENSITY ESTIMATES AND VARIABLE KERNEL DENSITY ESTIMATES0.40511100%
7George R. Terrell and David W. Scott (1992) Variable Kernel Density Estimation0.40511100%
8Chhor, Julien and Carpentier, Alexandra (2025) Local goodness-of-fit testing for Hölder-continuous densities: Minimax rates self0.40511100%
9Hecker, H (1976) A Characterization of the Asymptotic Normality of Linear Combinations of Order Statistics from the Uniform Distribution0.40511100%
10Mason, David M and Shorack, Galen R (1992) Necessary and sufficient conditions for asymptotic normality of L-statistics0.40511100%

Showing the top 10 of 16 scored citations.