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On weighted and locally polynomial directional quantile regression

Author

Listed:
  • Pavel Boček

    (Institute of Information Theory and Automation of the Czech Academy of Sciences)

  • Miroslav Šiman

    (Institute of Information Theory and Automation of the Czech Academy of Sciences)

Abstract

The article deals with certain quantile regression methods for vector responses. In particular, it describes weighted and locally polynomial extensions to the projectional quantile regression, discusses their properties, addresses their computational side, compares their outcome with recent analogous generalizations of the competing multiple-output directional quantile regression, demonstrates a link between the two competing methodologies, complements the results already available in the literature, illustrates the concepts with a few simulated and insightful examples illustrating some of their features, and shows their application to a real financial data set, namely to Forex 1M exchange rates. The real-data example strongly indicates that the presented methods might have a huge impact on the analysis of multivariate time series consisting of two to four dimensional observations.

Suggested Citation

  • Pavel Boček & Miroslav Šiman, 2017. "On weighted and locally polynomial directional quantile regression," Computational Statistics, Springer, vol. 32(3), pages 929-946, September.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-016-0708-9
    DOI: 10.1007/s00180-016-0708-9
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    References listed on IDEAS

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    1. Paindaveine, Davy & Siman, Miroslav, 2011. "On directional multiple-output quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 193-212, February.
    2. Davy Paindaveine & Germain Van bever, 2013. "From Depth to Local Depth: A Focus on Centrality," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1105-1119, September.
    3. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    5. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1529-1564, October.
    6. Davy Paindaveine & Miroslav Šiman, 2012. "Computing multiple-output regression quantile regions from projection quantiles," Computational Statistics, Springer, vol. 27(1), pages 29-49, March.
    7. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 459-470, September.
    8. Wei, Ying, 2008. "An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 397-409, March.
    9. Robert Serfling, 2002. "Quantile functions for multivariate analysis: approaches and applications," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 214-232, May.
    10. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(5), pages 793-813, December.
    11. Marc Hallin & Miroslav Šiman, 2016. "Multiple-Output Quantile Regression," Working Papers ECARES ECARES 2016-03, ULB -- Universite Libre de Bruxelles.
    12. Ioannides, D. A., 2004. "Fixed design regression quantiles for time series," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 235-245, July.
    13. Yu, Keming & Jones, M. C., 1997. "A comparison of local constant and local linear regression quantile estimators," Computational Statistics & Data Analysis, Elsevier, vol. 25(2), pages 159-166, July.
    14. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    15. Paindaveine, Davy & Šiman, Miroslav, 2012. "Computing multiple-output regression quantile regions," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 840-853.
    16. Keming Yu & Zudi Lu, 2004. "Local Linear Additive Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 333-346, September.
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    Cited by:

    1. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
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    3. Daniel Hlubinka & Lukáš Kotík & Miroslav Šiman, 2022. "Multivariate quantiles with both overall and directional probability interpretation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1586-1604, December.

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