IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i13p2011-d1424770.html
   My bibliography  Save this article

Varying Index Coefficient Model for Tail Index Regression

Author

Listed:
  • Hongyu An

    (School of Mathematics, Harbin Institute of Technology, Xidazhi, Harbin 150001, China)

  • Boping Tian

    (School of Mathematics, Harbin Institute of Technology, Xidazhi, Harbin 150001, China)

Abstract

Investigating the causes of extreme events is crucial across various fields. However, existing asymptotic theoretical models often lack flexibility and fail to capture the complex dependency structures inherent in extreme events. Additionally, the scarcity of extreme event data and the challenge of fully nonparametric estimation with high-dimensional covariates lead to the “curse of dimensionality”, complicating the analysis of extreme events. Considering the nonlinear interactions among covariates, we propose a flexible model that combines varying index coefficient models with extreme value theory to address these issues. This approach effectively avoids the curse of dimensionality while providing robust explanatory power and high flexibility. Our model also includes a variable selection process, for which we have demonstrated the consistency of the estimators and the oracle property of the variable selection. Monte Carlo simulation results validate the finite sample properties of the estimators. Furthermore, an empirical analysis of tail risk in financial markets offers valuable insights into the drivers of risk.

Suggested Citation

  • Hongyu An & Boping Tian, 2024. "Varying Index Coefficient Model for Tail Index Regression," Mathematics, MDPI, vol. 12(13), pages 1-34, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2011-:d:1424770
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/13/2011/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/13/2011/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. V. Chavez‐Demoulin & A. C. Davison, 2005. "Generalized additive modelling of sample extremes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 207-222, January.
    3. Beirlant, Jan & Goegebeur, Yuri, 2003. "Regression with response distributions of Pareto-type," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 595-619, April.
    4. Feng, Sanying & Xue, Liugen, 2015. "Model detection and estimation for single-index varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 227-244.
    5. Yaolan Ma & Yuexiang Jiang & Wei Huang, 2019. "Tail index varying coefficient model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(2), pages 235-256, January.
    6. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    8. Liu, Rong & Yang, Lijian, 2010. "Spline-Backfitted Kernel Smoothing Of Additive Coefficient Model," Econometric Theory, Cambridge University Press, vol. 26(1), pages 29-59, February.
    9. Johnson, Brent A. & Lin, D.Y. & Zeng, Donglin, 2008. "Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 672-680, June.
    10. 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.
    11. Wang, Hansheng & Tsai, Chih-Ling, 2009. "Tail Index Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1233-1240.
    12. Shujie Ma & Peter X.-K. Song, 2015. "Varying Index Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 341-356, March.
    Full references (including those not matched with items on IDEAS)

    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. Zhang, Qingzhao & Li, Deyuan & Wang, Hansheng, 2013. "A note on tail dependence regression," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 163-172.
    2. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    3. 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.
    4. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    5. Li, Xinyi & Wang, Li & Nettleton, Dan, 2019. "Sparse model identification and learning for ultra-high-dimensional additive partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 204-228.
    6. Yongjin Li & Qingzhao Zhang & Qihua Wang, 2017. "Penalized estimation equation for an extended single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 169-187, February.
    7. Zhangong Zhou & Rong Jiang & Weimin Qian, 2013. "LAD variable selection for linear models with randomly censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 287-300, February.
    8. Fan, Zengyan & Lian, Heng, 2018. "Quantile regression for additive coefficient models in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 54-64.
    9. Xingwei Tong & Xin He & Liuquan Sun & Jianguo Sun, 2009. "Variable Selection for Panel Count Data via Non‐Concave Penalized Estimating Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 620-635, December.
    10. Blommaert, A. & Hens, N. & Beutels, Ph., 2014. "Data mining for longitudinal data under multicollinearity and time dependence using penalized generalized estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 667-680.
    11. Yoshida, Takuma, 2018. "Semiparametric method for model structure discovery in additive regression models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 124-136.
    12. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," CeMMAP working papers 35/15, Institute for Fiscal Studies.
    13. Bingduo Yang & Christian M. Hafner & Guannan Liu & Wei Long, 2021. "Semiparametric estimation and variable selection for single‐index copula models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 962-988, November.
    14. Zangdong He & Wanzhu Tu & Sijian Wang & Haoda Fu & Zhangsheng Yu, 2015. "Simultaneous variable selection for joint models of longitudinal and survival outcomes," Biometrics, The International Biometric Society, vol. 71(1), pages 178-187, March.
    15. Jiawei Hou & Yunquan Song, 2022. "Interquantile shrinkage in spatial additive autoregressive models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1030-1057, December.
    16. Joel L. Horowitz, 2015. "Variable selection and estimation in high‐dimensional models," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(2), pages 389-407, May.
    17. Lu Tang & Peter X.‐K. Song, 2021. "Poststratification fusion learning in longitudinal data analysis," Biometrics, The International Biometric Society, vol. 77(3), pages 914-928, September.
    18. Wenning Feng & Abdhi Sarkar & Chae Young Lim & Tapabrata Maiti, 2016. "Variable selection for binary spatial regression: Penalized quasi‐likelihood approach," Biometrics, The International Biometric Society, vol. 72(4), pages 1164-1172, December.
    19. Peng Lai & Fangjian Wang & Tingyu Zhu & Qingzhao Zhang, 2021. "Model identification and selection for single-index varying-coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 457-480, June.
    20. Wang, Li & Wang, Suojin & Wang, Guannan, 2014. "Variable selection and estimation for longitudinal survey data," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 409-424.

    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:gam:jmathe:v:12:y:2024:i:13:p:2011-:d:1424770. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.