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Predicting pollution incidents through semiparametric quantile regression models

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Abstract

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.

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References

  • Abberger K (1998) Cross Validation in nonparametric quantile regression. Allg Stat Arch 82:149–161

    Google Scholar 

  • Bhattacharya PK, Gangopadhyay AK (1990) Kernel and nearest-neighbor estimation of a conditional quantile regression. Ann Stat 18:1400–1415

    Article  Google Scholar 

  • 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 123:759–765

    Article  CAS  Google Scholar 

  • Brian S, Cade B, Noon R (2003) A gentle introduction to quantile regression for ecologists. Front Ecol Environ 1:412–420

    Article  Google Scholar 

  • Cole TJ (1998) Using the LMS method to measure skewness in the NCHS and Dutch national height standards. Ann Hum Biol 16:407–419

    Article  Google Scholar 

  • Conde-Amboage M, Gonzlez-Manteiga W, Snchez-Seller C (2017) Predicting trace gas concentrations using quantile regression models. Stoch Environ Res Risk Assess 6:135–137

    Google Scholar 

  • Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96:1348–1360

    Article  Google Scholar 

  • Fan J, Marron JS (1994) Fast implementation of nonparametric curves estimators. J Comput Graph Stat 3:35–56

    Google Scholar 

  • Fan J, Hu TC, Truong YK (1994) Robust nonparametric function estimation. Scand J Stat 21:433–446

    Google Scholar 

  • Feng X, He X, Hu J (2001) Wild bootstrap for quantile regression. Biometrika 98:995–999

    Article  Google Scholar 

  • Horowitz JL, Lee S (2005) Nonparametric estimation of an additive quantile regression model. J Am Stat Assoc 100:1238–1249

    Article  CAS  Google Scholar 

  • Huang Q, Zhang H, Chen J, He M (2017) Quantile regression models and their applications: a review. J Biomet Biostat 8:801–817

    Article  Google Scholar 

  • Koenker K (2005) Quantile regression. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Koenker R (2011) Additive models for quantile regression: model selection and confidence bandaids. Braz J Probab Stat 25:239–262

    Article  Google Scholar 

  • Koenker RW, Bassett GW (1978) Regression quantiles. Econometrica 46:33–50

    Article  Google Scholar 

  • Koenker R, Pin NG P, Portnoy S (1994) Quantile smoothing splines. Biometrika 81:673–680

    Article  Google Scholar 

  • Lee YK, Mammen E, Park BY (2010) Backfitting and smooth backfitting for additive quantile models. Ann Stat 38:2857–2883

    Article  Google Scholar 

  • Mammen E (1993) Bootstrap and wild bootstrap for high dimensional linear models. Ann Stat 21:255–285

    Article  Google Scholar 

  • 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 27:147–157

    Article  CAS  Google Scholar 

  • 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 56:184–193

    Article  CAS  Google Scholar 

  • 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 77:647–665

    Article  CAS  Google Scholar 

  • Noh H, Lee NR (2014) Component selection in additive quantile regression models. J Korean Stat Soc 43:439–452

    Article  Google Scholar 

  • Reich BJ, Fuentes M, Dunson DB (2011) Bayesian spatial quantile regression. J Am Stat Assoc 106:6–20

    Article  CAS  Google Scholar 

  • Rose W, Deltas G, Khanna M (2004) Incentives for environmental self-regulation and implications for environmental performance. J Environ Econ Manag 1:632–654

    Google Scholar 

  • Ruppert D, Sheather SJ, Wand MP (1995) An effective bandwidth selector for local least squares regression. J Am Stat Assoc 90:1257–1270

    Article  Google Scholar 

  • Russell B, Dyer J (2017) Investigating the link between \(PM_{2.5}\) and atmospheric profile variables via penalized functional quantile regression. Environ Ecol Stat 24:363–384

    Article  CAS  Google Scholar 

  • Sun Y (2006) A consistent nonparametric equality test of conditional quantile estimation. Econ Theory 22:614–632

    Article  Google Scholar 

  • Wu Y, Liu Y (2009) Variable selection in quantile regression. Stat Sin 19:801–817

    Google Scholar 

  • Yu K, Jones MC (1998) Local linear quantile regression. J Am Stat Assoc 93:228–237

    Article  Google Scholar 

  • Yu K, Lu Z (2004) Local linear additive quantile regression. Scand J Stat 31:333–346

    Article  Google Scholar 

  • Yu K, Lu Z, Stander J (2003) Quantile regression: applications and current research areas. Stat R Stat Soc 52:331–350

    Article  Google Scholar 

  • Zhu L, Huang M, Li R (2012) Semiparametric quantile regression with high-dimensional covariates. Stat Sin 22:1379–1401

    Google Scholar 

  • Zhu Q, Hu Y, Tian M (2017) Identifying interaction effects via additive quantile regression models. Stat Interface 10:255–265

    Article  Google Scholar 

  • Zou H, Yuanb M (2008) Regularized simultaneous model selection in multiple quantiles regression. Comput Stat Data Anal 52:5296–5304

    Article  Google Scholar 

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Acknowledgements

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).

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Correspondence to C. Ordóñez.

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Roca-Pardiñas, J., Ordóñez, C. Predicting pollution incidents through semiparametric quantile regression models. Stoch Environ Res Risk Assess 33, 673–685 (2019). https://doi.org/10.1007/s00477-019-01653-7

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