Predicting pollution incidents through semiparametric quantile regression models

  • J. Roca-Pardiñas
  • C. OrdóñezEmail author
Original Paper


In this paper we present a method to forecast pollution episodes using measurements of the pollutant concentration along time. Specifically, we use a backfitting algorithm with local polynomial kernel smoothers to estimate a semiparametric additive quantile regression model. We also propose a statistical hypothesis test to determine critical values, i.e., the values of the concentration that are significant to forecast the pollution episodes. This test is based on a wild bootstrap approach modified to suit asymmetric loss functions, as occurs in quantile regression. The validity of the method was checked with both simulated and real data, the latter from \({\hbox {SO}}_{2}\) emissions from a coal-fired power station located in Northern Spain.


\({\hbox {SO}}_{2}\) pollution incidents Kernel smoothers Quantile regression Wild bootstrap 



This paper has been supported by projects: (1) Avances metodológicos y computacionales en estadística no-paramétrica y semiparamétrica—Ministerio de Ciencia e Investigación (MTM2014-55966-P) and (2) Nuevos avances metodológicos y computationales en estadística no paramétrica y semiparamétrica—Ministerio de Economía, Industria y Competitividad (MTM2017-89422-P).


  1. Abberger K (1998) Cross Validation in nonparametric quantile regression. Allg Stat Arch 82:149–161Google Scholar
  2. Bhattacharya PK, Gangopadhyay AK (1990) Kernel and nearest-neighbor estimation of a conditional quantile regression. Ann Stat 18:1400–1415CrossRefGoogle Scholar
  3. Bind MAC, Coull BA, Peters A, Baccarelli A, Tarantini L, Cantone L, Vokonas PS, Koutrakis P, Schwartz JD (2015) Beyond the mean: quantile regression to explore the association of air pollution with gene-specific methylation in the normative aging study. Environ Health Perspect 123:759–765CrossRefGoogle Scholar
  4. Brian S, Cade B, Noon R (2003) A gentle introduction to quantile regression for ecologists. Front Ecol Environ 1:412–420CrossRefGoogle Scholar
  5. Cole TJ (1998) Using the LMS method to measure skewness in the NCHS and Dutch national height standards. Ann Hum Biol 16:407–419CrossRefGoogle Scholar
  6. Conde-Amboage M, Gonzlez-Manteiga W, Snchez-Seller C (2017) Predicting trace gas concentrations using quantile regression models. Stoch Environ Res Risk Assess 6:135–137Google Scholar
  7. Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96:1348–1360CrossRefGoogle Scholar
  8. Fan J, Marron JS (1994) Fast implementation of nonparametric curves estimators. J Comput Graph Stat 3:35–56Google Scholar
  9. Fan J, Hu TC, Truong YK (1994) Robust nonparametric function estimation. Scand J Stat 21:433–446Google Scholar
  10. Feng X, He X, Hu J (2001) Wild bootstrap for quantile regression. Biometrika 98:995–999CrossRefGoogle Scholar
  11. Horowitz JL, Lee S (2005) Nonparametric estimation of an additive quantile regression model. J Am Stat Assoc 100:1238–1249CrossRefGoogle Scholar
  12. Huang Q, Zhang H, Chen J, He M (2017) Quantile regression models and their applications: a review. J Biomet Biostat 8:801–817CrossRefGoogle Scholar
  13. Koenker K (2005) Quantile regression. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  14. Koenker R (2011) Additive models for quantile regression: model selection and confidence bandaids. Braz J Probab Stat 25:239–262CrossRefGoogle Scholar
  15. Koenker RW, Bassett GW (1978) Regression quantiles. Econometrica 46:33–50CrossRefGoogle Scholar
  16. Koenker R, Pin NG P, Portnoy S (1994) Quantile smoothing splines. Biometrika 81:673–680CrossRefGoogle Scholar
  17. Lee YK, Mammen E, Park BY (2010) Backfitting and smooth backfitting for additive quantile models. Ann Stat 38:2857–2883CrossRefGoogle Scholar
  18. Mammen E (1993) Bootstrap and wild bootstrap for high dimensional linear models. Ann Stat 21:255–285CrossRefGoogle Scholar
  19. Martínez-Silva I, Roca-Pardiñas J, Ordóñez C (2016) Forecasting \({\text{ SO }}_2\) pollution incidents by means of quantile curves based on additive models. Environmetrics 27:147–157CrossRefGoogle Scholar
  20. Monteiroa A, Carvalho A, Ribeiro I, Scotto M, Barbosa S, Alonso A, Baldasano JM, Pay MT, Miranda AI, Borregoan C (2012) Trends in ozone concentrations in the Iberian Peninsula by quantile regression and clustering. Atmos Environ 56:184–193CrossRefGoogle Scholar
  21. Munir S, Habeebullah TM, Abdulaziz R, Safwat S, Atif MF, Morsy E (2013) Quantifying temporal trends of atmospheric pollutants in Makkah (1997–2012). Atmos Environ 77:647–665CrossRefGoogle Scholar
  22. Noh H, Lee NR (2014) Component selection in additive quantile regression models. J Korean Stat Soc 43:439–452CrossRefGoogle Scholar
  23. Reich BJ, Fuentes M, Dunson DB (2011) Bayesian spatial quantile regression. J Am Stat Assoc 106:6–20CrossRefGoogle Scholar
  24. Rose W, Deltas G, Khanna M (2004) Incentives for environmental self-regulation and implications for environmental performance. J Environ Econ Manag 1:632–654Google Scholar
  25. Ruppert D, Sheather SJ, Wand MP (1995) An effective bandwidth selector for local least squares regression. J Am Stat Assoc 90:1257–1270CrossRefGoogle Scholar
  26. Russell B, Dyer J (2017) Investigating the link between \(PM_{2.5}\) and atmospheric profile variables via penalized functional quantile regression. Environ Ecol Stat 24:363–384CrossRefGoogle Scholar
  27. Sun Y (2006) A consistent nonparametric equality test of conditional quantile estimation. Econ Theory 22:614–632CrossRefGoogle Scholar
  28. Wu Y, Liu Y (2009) Variable selection in quantile regression. Stat Sin 19:801–817Google Scholar
  29. Yu K, Jones MC (1998) Local linear quantile regression. J Am Stat Assoc 93:228–237CrossRefGoogle Scholar
  30. Yu K, Lu Z (2004) Local linear additive quantile regression. Scand J Stat 31:333–346CrossRefGoogle Scholar
  31. Yu K, Lu Z, Stander J (2003) Quantile regression: applications and current research areas. Stat R Stat Soc 52:331–350CrossRefGoogle Scholar
  32. Zhu L, Huang M, Li R (2012) Semiparametric quantile regression with high-dimensional covariates. Stat Sin 22:1379–1401Google Scholar
  33. Zhu Q, Hu Y, Tian M (2017) Identifying interaction effects via additive quantile regression models. Stat Interface 10:255–265CrossRefGoogle Scholar
  34. Zou H, Yuanb M (2008) Regularized simultaneous model selection in multiple quantiles regression. Comput Stat Data Anal 52:5296–5304CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of VigoVigoSpain
  2. 2.Department of Mining Exploitation and ProspectingUniversity of OviedoOviedoSpain

Personalised recommendations