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Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics

Author

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  • Matt Goldman
  • David M. Kaplan

Abstract

We provide novel, high‐order accurate methods for non‐parametric inference on quantile differences between two populations in both unconditional and conditional settings. These quantile differences correspond to (conditional) quantile treatment effects under (conditional) independence of a binary treatment and potential outcomes. Our methods use the probability integral transform and a Dirichlet (rather than Gaussian) reference distribution to pick appropriate L‐statistics as confidence interval endpoints, achieving high‐order accuracy. Using a similar approach, we also propose confidence intervals/sets for vectors of quantiles, interquantile ranges and differences of linear combinations of quantiles. In the conditional setting, when smoothing over continuous covariates, optimal bandwidth and coverage probability rates are derived for all methods. Simulations show that the new confidence intervals have a favourable combination of robust accuracy and short length compared with existing approaches. Detailed steps for confidence interval construction are provided in online Appendix E as supporting information, and code for all methods, simulations and empirical examples is provided.

Suggested Citation

  • Matt Goldman & David M. Kaplan, 2018. "Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 136-169, June.
    • Handle: RePEc:wly:emjrnl:v:21:y:2018:i:2:p:136-169
    DOI: 10.1111/ectj.12095
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    Cited by:

    1. Mototsugu Fukushige & Yingxin Shi, 2022. "Quantile regression approach for measuring production inefficiency with empirical application to the primary production sector for the Xinjiang Production and Construction Corps in China," Asia-Pacific Journal of Regional Science, Springer, vol. 6(2), pages 777-805, June.
    2. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    3. Cui-Juan Kong & Han-Ying Liang, 2024. "Quantile difference estimation with censoring indicators missing at random," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(2), pages 345-382, April.
    4. Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
    5. David M. Kaplan, 2014. "Nonparametric Inference on Quantile Marginal Effects," Working Papers 1413, Department of Economics, University of Missouri.
    6. Goldman, Matt & Kaplan, David M., 2017. "Fractional order statistic approximation for nonparametric conditional quantile inference," Journal of Econometrics, Elsevier, vol. 196(2), pages 331-346.

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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