IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v30y2014i06p1272-1314_00.html
   My bibliography  Save this article

Efficient Regressions Via Optimally Combining Quantile Information

Author

Listed:
  • Zhao, Zhibiao
  • Xiao, Zhijie

Abstract

We develop a generally applicable framework for constructing efficient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a fixed number of quantiles, we derive an upper bound on the distance between the efficiency of the proposed estimator and the Fisher information. As the number of quantiles increases, this upper bound decreases and the asymptotic variance of the proposed estimator approaches the Cramér–Rao lower bound under appropriate conditions. In the case of nonregular statistical estimation, the proposed estimator leads to super-efficient estimation. We illustrate the proposed method for several widely used regression models. Both asymptotic theory and Monte Carlo experiments show the superior performance over existing methods.

Suggested Citation

  • Zhao, Zhibiao & Xiao, Zhijie, 2014. "Efficient Regressions Via Optimally Combining Quantile Information," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1272-1314, December.
  • Handle: RePEc:cup:etheor:v:30:y:2014:i:06:p:1272-1314_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466614000176/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    2. Lima, Luiz Renato & Meng, Fanning & Godeiro, Lucas, 2020. "Quantile forecasting with mixed-frequency data," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1149-1162.
    3. Hasan A. Fallahgoul & David Veredas & Frank J. Fabozzi, 2019. "Quantile-Based Inference for Tempered Stable Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 51-83, January.
    4. Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    5. Yingying Hu & Huixia Judy Wang & Xuming He & Jianhua Guo, 2021. "Bayesian joint-quantile regression," Computational Statistics, Springer, vol. 36(3), pages 2033-2053, September.
    6. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    7. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.
    8. Cho, Hyunkeun & Kim, Seonjin & Kim, Mi-Ok, 2017. "Multiple quantile regression analysis of longitudinal data: Heteroscedasticity and efficient estimation," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 334-343.
    9. Kangning Wang & Lu Lin, 2017. "Robust and efficient direction identification for groupwise additive multiple-index models and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 22-45, March.
    10. He, Qianchuan & Kong, Linglong & Wang, Yanhua & Wang, Sijian & Chan, Timothy A. & Holland, Eric, 2016. "Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 222-239.
    11. Feiyu Jiang & Zifeng Zhao & Xiaofeng Shao, 2022. "Jiang, Zhao and Shao's reply to the Discussion of ‘The First Discussion Meeting on Statistical Aspects of the Covid‐19 Pandemic’," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1849-1854, October.
    12. Ozcan, Burcu & Temiz, Mehmet & Gültekin Tarla, Esma, 2023. "The resource curse phenomenon in the case of precious metals: A panel evidence from top 19 exporting countries," Resources Policy, Elsevier, vol. 81(C).
    13. Y. Andriyana & I. Gijbels & A. Verhasselt, 2018. "Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity," Statistical Papers, Springer, vol. 59(4), pages 1589-1621, December.
    14. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    15. Aiai Yu & Yujie Zhong & Xingdong Feng & Ying Wei, 2023. "Quantile regression for nonignorable missing data with its application of analyzing electronic medical records," Biometrics, The International Biometric Society, vol. 79(3), pages 2036-2049, September.
    16. Xiao Huang & Zhaoguo Zhan, 2022. "Local Composite Quantile Regression for Regression Discontinuity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1863-1875, October.
    17. Wang, Chuan-Sheng & Zhao, Zhibiao, 2016. "Conditional Value-at-Risk: Semiparametric estimation and inference," Journal of Econometrics, Elsevier, vol. 195(1), pages 86-103.
    18. Erik Figueiredo & Luiz Renato Lima, 2020. "Do economic integration agreements affect trade predictability? A group effect analysis," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 637-664, May.
    19. Zhu, Ke, 2023. "A new generalized exponentially weighted moving average quantile model and its statistical inference," Journal of Econometrics, Elsevier, vol. 237(1).
    20. WenWu Wang & Ping Yu, 2023. "Nonequivalence of two least-absolute-deviation estimators for mediation effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 370-387, March.
    21. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    22. Jing Sun, 2020. "An improvement on the efficiency of complete-case-analysis with nonignorable missing covariate data," Computational Statistics, Springer, vol. 35(4), pages 1621-1636, December.
    23. Seonjin Kim, 2015. "Hypothesis Testing For Arch Models: A Multiple Quantile Regressions Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 26-38, January.
    24. Sun, Jing & Sun, Qihang, 2015. "An improved and efficient estimation method for varying-coefficient model with missing covariates," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 296-303.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:30:y:2014:i:06:p:1272-1314_00. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.