IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v108y2013i503p1062-1074.html
   My bibliography  Save this article

Estimation of Extreme Conditional Quantiles Through Power Transformation

Author

Listed:
  • Huixia Judy Wang
  • Deyuan Li

Abstract

The estimation of extreme conditional quantiles is an important issue in numerous disciplines. Quantile regression (QR) provides a natural way to capture the covariate effects at different tails of the response distribution. However, without any distributional assumptions, estimation from conventional QR is often unstable at the tails, especially for heavy-tailed distributions due to data sparsity. In this article, we develop a new three-stage estimation procedure that integrates QR and extreme value theory by estimating intermediate conditional quantiles using QR and extrapolating these estimates to tails based on extreme value theory. Using the power-transformed QR, the proposed method allows more flexibility than existing methods that rely on the linearity of quantiles on the original scale, while extending the applicability of parametric models to borrow information across covariates without resorting to nonparametric smoothing. In addition, we propose a test procedure to assess the commonality of extreme value index, which could be useful for obtaining more efficient estimation by sharing information across covariates. We establish the asymptotic properties of the proposed method and demonstrate its value through simulation study and the analysis of a medical cost data. Supplementary materials for this article are available online.

Suggested Citation

  • Huixia Judy Wang & Deyuan Li, 2013. "Estimation of Extreme Conditional Quantiles Through Power Transformation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1062-1074, September.
  • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:1062-1074
    DOI: 10.1080/01621459.2013.820134
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2013.820134
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2013.820134?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yin, Guosheng & Zeng, Donglin & Li, Hui, 2008. "Power-Transformed Linear Quantile Regression With Censored Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1214-1224.
    2. Huixia Judy Wang & Deyuan Li & Xuming He, 2012. "Estimation of High Conditional Quantiles for Heavy-Tailed Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1453-1464, December.
    3. Gomes, M. Ivette & Pestana, Dinis, 2007. "A Sturdy Reduced-Bias Extreme Quantile (VaR) Estimator," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 280-292, March.
    4. Mu, Yunming & He, Xuming, 2007. "Power Transformation Toward a Linear Regression Quantile," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 269-279, March.
    5. He X. & Zhu L-X., 2003. "A Lack-of-Fit Test for Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1013-1022, January.
    6. Duan, Naihua, et al, 1983. "A Comparison of Alternative Models for the Demand for Medical Care," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 115-126, April.
    7. Wang, Hansheng & Tsai, Chih-Ling, 2009. "Tail Index Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1233-1240.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Karlsson, Martin & Wang, Yulong & Ziebarth, Nicolas R., 2024. "Getting the right tail right: Modeling tails of health expenditure distributions," Journal of Health Economics, Elsevier, vol. 97(C).
    2. 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.
    3. 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.
    4. Ji Hyung Lee & Yuya Sasaki & Alexis Akira Toda & Yulong Wang, 2021. "Fixed-k Tail Regression: New Evidence on Tax and Wealth Inequality from Forbes 400," Papers 2105.10007, arXiv.org, revised Sep 2022.
    5. Bissan Ghaddar & Ignacio Gómez-Casares & Julio González-Díaz & Brais González-Rodríguez & Beatriz Pateiro-López & Sofía Rodríguez-Ballesteros, 2023. "Learning for Spatial Branching: An Algorithm Selection Approach," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1024-1043, September.
    6. Chen, Zhao & Cheng, Vivian Xinyi & Liu, Xu, 2024. "Hypothesis testing on high dimensional quantile regression," Journal of Econometrics, Elsevier, vol. 238(1).
    7. Hou, Yanxi & Leng, Xuan & Peng, Liang & Zhou, Yinggang, 2024. "Panel quantile regression for extreme risk," Journal of Econometrics, Elsevier, vol. 240(1).
    8. Yingying Hu & Huixia Judy Wang & Xuming He & Jianhua Guo, 2021. "Bayesian joint-quantile regression," Computational Statistics, Springer, vol. 36(3), pages 2033-2053, September.
    9. Chen, Zhao & Cheng, Vivian Xinyi & Liu, Xu, 2024. "Reprint: Hypothesis testing on high dimensional quantile regression," Journal of Econometrics, Elsevier, vol. 239(2).
    10. Mei Ling Huang & Christine Nguyen, 2018. "A nonparametric approach for quantile regression," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-14, December.
    11. Sottile, Gianluca & Frumento, Paolo, 2022. "Robust estimation and regression with parametric quantile functions," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    12. Yuya Sasaki & Yulong Wang, 2022. "Fixed-k Inference for Conditional Extremal Quantiles," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 829-837, April.
    13. Yaolan Ma & Bo Wei & Wei Huang, 2020. "A nonparametric estimator for the conditional tail index of Pareto-type distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 17-44, January.
    14. Norman Maswanganyi & Caston Sigauke & Edmore Ranganai, 2021. "Prediction of Extreme Conditional Quantiles of Electricity Demand: An Application Using South African Data," Energies, MDPI, vol. 14(20), pages 1-21, October.
    15. Hao, Meiling & Lin, Yuanyuan & Shen, Guohao & Su, Wen, 2023. "Nonparametric inference on smoothed quantile regression process," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    16. Silvia Sarpietro & Yuya Sasaki & Yulong Wang, 2022. "Non-Existent Moments of Earnings Growth," Papers 2203.08014, arXiv.org, revised Feb 2024.
    17. Stéphane Girard & Gilles Claude Stupfler & Antoine Usseglio-Carleve, 2021. "Extreme Conditional Expectile Estimation in Heavy-Tailed Heteroscedastic Regression Models," Post-Print hal-03306230, HAL.
    18. Georgios Tsiotas, 2020. "On the use of power transformations in CAViaR models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 296-312, March.
    19. Ma, Yaolan & Jiang, Yuexiang & Huang, Wei, 2018. "Empirical likelihood based inference for conditional Pareto-type tail index," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 114-121.
    20. Takuma Yoshida, 2021. "Additive models for extremal quantile regression with Pareto-type distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 103-134, March.
    21. He, Fengyang & Wang, Huixia Judy & Zhou, Yuejin, 2022. "Extremal quantile autoregression for heavy-tailed time series," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2014. "Local robust and asymptotically unbiased estimation of conditional Pareto-type tails," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 330-355, June.
    2. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
    3. Luke B. Smith & Brian J. Reich & Amy H. Herring & Peter H. Langlois & Montserrat Fuentes, 2015. "Multilevel quantile function modeling with application to birth outcomes," Biometrics, The International Biometric Society, vol. 71(2), pages 508-519, June.
    4. He, Fengyang & Wang, Huixia Judy & Zhou, Yuejin, 2022. "Extremal quantile autoregression for heavy-tailed time series," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    5. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Inference for extremal regression with dependent heavy-tailed data," TSE Working Papers 22-1324, Toulouse School of Economics (TSE), revised 29 Aug 2023.
    6. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    7. Ruosha Li & Yu Cheng & Jason P. Fine, 2014. "Quantile Association Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 230-242, March.
    8. Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2021. "Local Robust Estimation of Pareto-Type Tails with Random Right Censoring," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 70-108, February.
    9. Tong Siu Tung Wong & Wai Keung Li, 2015. "Extreme values identification in regression using a peaks-over-threshold approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 566-576, March.
    10. Jonathan El Methni & Laurent Gardes & Stéphane Girard, 2014. "Non-parametric Estimation of Extreme Risk Measures from Conditional Heavy-tailed Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 988-1012, December.
    11. Hao, Meiling & Lin, Yuanyuan & Shen, Guohao & Su, Wen, 2023. "Nonparametric inference on smoothed quantile regression process," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    12. Jin-Jian Hsieh & Hong-Rui Wang, 2018. "Quantile regression based on counting process approach under semi-competing risks data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 395-419, April.
    13. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    14. Shi, Peng & Frees, Edward W., 2010. "Long-tail longitudinal modeling of insurance company expenses," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 303-314, December.
    15. Zhang, Qingzhao & Li, Deyuan & Wang, Hansheng, 2013. "A note on tail dependence regression," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 163-172.
    16. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    17. John H. J. Einmahl & Fan Yang & Chen Zhou, 2021. "Testing the Multivariate Regular Variation Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 907-919, October.
    18. Koki Momoki & Takuma Yoshida, 2024. "Hypothesis testing for varying coefficient models in tail index regression," Statistical Papers, Springer, vol. 65(6), pages 3821-3852, August.
    19. Yang Lu, 2019. "Flexible (panel) regression models for bivariate count–continuous data with an insurance application," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1503-1521, October.
    20. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.

    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:taf:jnlasa:v:108:y:2013:i:503:p:1062-1074. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.