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Flexible quantile contour estimation for multivariate functional data: Beyond convexity

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  • Agarwal, Gaurav
  • Tu, Wei
  • Sun, Ying
  • Kong, Linglong

Abstract

Nowadays, multivariate functional data are frequently observed in many scientific fields, and the estimation of quantiles of these data is essential in data analysis. Unlike in the univariate setting, quantiles are more challenging to estimate for multivariate data, let alone multivariate functional data. This article proposes a new method to estimate the quantiles for multivariate functional data with application to air pollution data. The proposed multivariate functional quantile model is a nonparametric, time-varying coefficient model, and basis functions are used for the estimation and prediction. The estimated quantile contours can account for non-Gaussian and even nonconvex features of the multivariate distributions marginally, and the estimated multivariate quantile function is a continuous function of time for a fixed quantile level. Computationally, the proposed method is shown to be efficient for both bivariate and trivariate functional data. The monotonicity, uniqueness, and consistency of the estimated multivariate quantile function have been established. The proposed method was demonstrated on bivariate and trivariate functional data in the simulation studies, and was applied to study the joint distribution of PM2.5 and geopotential height over time in the Northeastern United States; the estimated contours highlight the nonconvex features of the joint distribution, and the functional quantile curves capture the dynamic change across time.

Suggested Citation

  • Agarwal, Gaurav & Tu, Wei & Sun, Ying & Kong, Linglong, 2022. "Flexible quantile contour estimation for multivariate functional data: Beyond convexity," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:csdana:v:168:y:2022:i:c:s0167947321002346
    DOI: 10.1016/j.csda.2021.107400
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    1. Bucher, Axel & Segers, Johan & Volgushev, Stanislav, 2014. "When uniform weak convergence fails: empirical processes for dependence functions via epi- and hypographs," LIDAM Reprints ISBA 2014018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Biman Chakraborty, 2001. "On Affine Equivariant Multivariate Quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 380-403, June.
    3. Brook T. Russell & Dewei Wang & Christopher S. McMahan, 2017. "Spatially modeling the effects of meteorological drivers of PM2.5 in the Eastern United States via a local linear penalized quantile regression estimator," Environmetrics, John Wiley & Sons, Ltd., vol. 28(5), August.
    4. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    5. Robert Serfling, 2010. "Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 915-936.
    6. 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.
    7. Davy Paindaveine & Miroslav Šiman, 2012. "Computing multiple-output regression quantile regions from projection quantiles," Computational Statistics, Springer, vol. 27(1), pages 29-49, March.
    8. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015. "Vector quantile regression: an optimal transport approach," CeMMAP working papers 58/15, Institute for Fiscal Studies.
    9. 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.
    10. Liu, Xiaohui & Zuo, Yijun & Wang, Zhizhong, 2013. "Exactly computing bivariate projection depth contours and median," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 1-11.
    11. Serfling, Robert & Wijesuriya, Uditha, 2017. "Depth-based nonparametric description of functional data, with emphasis on use of spatial depth," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 24-45.
    12. Breckling, Jens & Kokic, Philip & Lübke, Oliver, 2001. "A note on multivariate M-quantiles," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 39-44, November.
    13. Montserrat Fuentes & Hae-Ryoung Song & Sujit K. Ghosh & David M. Holland & Jerry M. Davis, 2006. "Spatial Association between Speciated Fine Particles and Mortality," Biometrics, The International Biometric Society, vol. 62(3), pages 855-863, September.
    14. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    15. repec:hal:spmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
    16. Fraiman, Ricardo & Pateiro-López, Beatriz, 2012. "Quantiles for finite and infinite dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 1-14.
    17. Paindaveine, Davy & Šiman, Miroslav, 2012. "Computing multiple-output regression quantile regions," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 840-853.
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