IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/33469.html
   My bibliography  Save this paper

A quantile based dimension reduction technique

Author

Listed:
  • Méndez Civieta, Álvaro
  • Aguilera Morillo, María del Carmen
  • Lillo Rodríguez, Rosa Elvira

Abstract

Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which are extremely sensitive to the presence of outliers or heavy tailed distributions. In contrast, quantile regression is an alternative to OLS that computes robust quantile based estimates. In this work, the multivariate PLS is extended to the quantile regression framework, obtaining a theoretical formulation of the problem and a robust dimensionality reduction technique that we call fast partial quantile regression (fPQR), that provides quantilebased estimates. An efficient implementation of fPQR is also derived, and its performance is studied through simulation experiments and the chemometrics well known biscuit dough dataset, a real high dimensional example.

Suggested Citation

  • Méndez Civieta, Álvaro & Aguilera Morillo, María del Carmen & Lillo Rodríguez, Rosa Elvira, 2021. "A quantile based dimension reduction technique," DES - Working Papers. Statistics and Econometrics. WS 33469, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:33469
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/251c42c3-2ad2-401f-a99b-775e532ced98/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Yadolah Dodge & Joe Whittaker, 2009. "Partial quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 35-57, June.
    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. Chao Xu & Jinchuan Ke & Xiaojun Zhao & Xiaofang Zhao, 2020. "Multiscale Quantile Correlation Coefficient: Measuring Tail Dependence of Financial Time Series," Sustainability, MDPI, vol. 12(12), pages 1-24, June.
    2. Bolós, V.J. & Benítez, R. & Ferrer, R. & Jammazi, R., 2017. "The windowed scalogram difference: A novel wavelet tool for comparing time series," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 49-65.
    3. Syed jawad hussain Shahzad & Saba Ameer & Muhammad Shahbaz, 2016. "Disaggregating the correlation under bearish and bullish markets: A Quantile-quantile approach," Economics Bulletin, AccessEcon, vol. 36(4), pages 2465-2473.
    4. Xiaochao Xia & Hao Ming, 2022. "A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation," Mathematics, MDPI, vol. 10(24), pages 1-32, December.
    5. Zhang, Shucong & Zhou, Yong, 2018. "Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 1-13.
    6. Ji-Eun Choi & Dong Wan Shin, 2022. "Quantile correlation coefficient: a new tail dependence measure," Statistical Papers, Springer, vol. 63(4), pages 1075-1104, August.
    7. Giglio, Stefano & Kelly, Bryan & Pruitt, Seth, 2016. "Systemic risk and the macroeconomy: An empirical evaluation," Journal of Financial Economics, Elsevier, vol. 119(3), pages 457-471.
    8. Yuzhu Tian & Manlai Tang & Yanchao Zang & Maozai Tian, 2018. "Quantile regression for linear models with autoregressive errors using EM algorithm," Computational Statistics, Springer, vol. 33(4), pages 1605-1625, December.
    9. Labidi, Chiaz & Rahman, Md Lutfur & Hedström, Axel & Uddin, Gazi Salah & Bekiros, Stelios, 2018. "Quantile dependence between developed and emerging stock markets aftermath of the global financial crisis," International Review of Financial Analysis, Elsevier, vol. 59(C), pages 179-211.
    10. Yundong Tu & Siwei Wang, 2023. "Variable Screening and Model Averaging for Expectile Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 574-598, June.
    11. Kumar, Anoop S & Padakandla, Steven Raj, 2022. "Testing the safe-haven properties of gold and bitcoin in the backdrop of COVID-19: A wavelet quantile correlation approach," Finance Research Letters, Elsevier, vol. 47(PB).
    12. Zhu, Xuening & Wang, Weining & Wang, Hansheng & Härdle, Wolfgang Karl, 2019. "Network quantile autoregression," Journal of Econometrics, Elsevier, vol. 212(1), pages 345-358.
    13. Tobias Fissler & Marc-Oliver Pohle, 2023. "Generalised Covariances and Correlations," Papers 2307.03594, arXiv.org, revised Sep 2023.
    14. Heejoon Han, 2016. "Quantile Dependence between Stock Markets and its Application in Volatility Forecasting," Papers 1608.07193, arXiv.org.
    15. Alqaralleh, Huthaifa & Canepa, Alessandra, 2022. "The role of precious metals in portfolio diversification during the Covid19 pandemic: A wavelet-based quantile approach," Resources Policy, Elsevier, vol. 75(C).
    16. Gkillas, Konstantinos & Boako, Gideon & Vortelinos, Dimitrios & Vasiliadis, Lavrentios, 2020. "Non-parametric quantile dependencies between volatility discontinuities and political risk," Finance Research Letters, Elsevier, vol. 32(C).
    17. Xiaolin Chen & Xiaojing Chen & Yi Liu, 2019. "A note on quantile feature screening via distance correlation," Statistical Papers, Springer, vol. 60(5), pages 1741-1762, October.
    18. Songqiao Tang & Huiyu Wang & Guanao Yan & Lixin Zhang, 2023. "Empirical likelihood based tests for detecting the presence of significant predictors in marginal quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(2), pages 149-179, February.
    19. Kumar, Anoop S & Padakandla, Steven Raj, 2023. "Do NFTs act as a good hedge and safe haven against Cryptocurrency fluctuations?," Finance Research Letters, Elsevier, vol. 56(C).
    20. Ladislav Kristoufek, 2020. "Grandpa, grandpa, tell me the one about Bitcoin being a safe haven: Evidence from the COVID-19 pandemics," Papers 2004.00047, arXiv.org.

    More about this item

    Keywords

    Partial-Least-Squares;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cte:wsrepe:33469. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.