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A direct approach to inference in nonparametric and semiparametric quantile models

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  • Fan, Yanqin
  • Liu, Ruixuan

Abstract

We construct a generic confidence interval for a conditional quantile via the direct approach. It avoids estimating the conditional density function of the dependent variable given the covariate and is asymptotically valid for any conditional quantile, any conditional quantile estimator, and any data structure, provided that certain weak convergence of the conditional quantile process holds for the original quantile estimator. We also construct a generic confidence band for the conditional quantile function across a range of covariate values. By using Yang–Stute estimator and two semiparametric quantile functions, we demonstrate the flexibility and simplicity of the direct approach. The advantages of our new confidence intervals are borne out in a simulation study.

Suggested Citation

  • Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
  • Handle: RePEc:eee:econom:v:191:y:2016:i:1:p:196-216
    DOI: 10.1016/j.jeconom.2015.01.009
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    Cited by:

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    2. Wenjun Chu & Shanglei Chai & Xi Chen & Mo Du, 2020. "Does the Impact of Carbon Price Determinants Change with the Different Quantiles of Carbon Prices? Evidence from China ETS Pilots," Sustainability, MDPI, Open Access Journal, vol. 12(14), pages 1-19, July.
    3. Chiang, Harold D. & Hsu, Yu-Chin & Sasaki, Yuya, 2019. "Robust uniform inference for quantile treatment effects in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 211(2), pages 589-618.
    4. 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.
    5. Fernandes, Marcelo & Guerre, Emmanuel & Horta, Eduardo, 2017. "Smoothing quantile regressions," Textos para discussão 457, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    6. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.
    7. 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.
    8. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.
    9. J. C. Escanciano & S. C. Goh, 2019. "Quantile-Regression Inference With Adaptive Control of Size," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1382-1393, July.

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    More about this item

    Keywords

    Generic confidence interval; Generic confidence band; Partially linear quantile regression; Single-index quantile regression; Rearranged quantile curve;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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