IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v201y2020ics0951832019300638.html
   My bibliography  Save this article

A review on quantile regression for stochastic computer experiments

Author

Listed:
  • Torossian, Léonard
  • Picheny, Victor
  • Faivre, Robert
  • Garivier, Aurélien

Abstract

We report on an empirical study of the main strategies for quantile regression in the context of stochastic computer experiments. To ensure adequate diversity, six metamodels are presented, divided into three categories based on order statistics, functional approaches, and those of Bayesian inspiration. The metamodels are tested on several problems characterized by the size of the training set, the input dimension, the signal-to-noise ratio and the value of the probability density function at the targeted quantile. The metamodels studied reveal good contrasts in our set of experiments, enabling several patterns to be extracted. Based on our results, guidelines are proposed to allow users to select the best method for a given problem.

Suggested Citation

  • Torossian, Léonard & Picheny, Victor & Faivre, Robert & Garivier, Aurélien, 2020. "A review on quantile regression for stochastic computer experiments," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:reensy:v:201:y:2020:i:c:s0951832019300638
    DOI: 10.1016/j.ress.2020.106858
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832019300638
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2020.106858?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Efromovich, Sam, 2010. "Dimension Reduction and Adaptation in Conditional Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 761-774.
    4. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    5. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    6. Janis Janusevskis & Rodolphe Le Riche, 2013. "Simultaneous kriging-based estimation and optimization of mean response," Journal of Global Optimization, Springer, vol. 55(2), pages 313-336, February.
    7. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).
    8. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Example results," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 55-77.
    9. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    10. Taddy, Matthew A. & Kottas, Athanasios, 2010. "A Bayesian Nonparametric Approach to Inference for Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 357-369.
    11. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Description of techniques," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 28-54.
    12. Victor Picheny & Ronan Trépos & Pierre Casadebaig, 2017. "Optimization of black-box models with uncertain climatic inputs—Application to sunflower ideotype design," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-15, May.
    13. Andreas Christmann & Ingo Steinwart, 2008. "Consistency of kernel‐based quantile regression," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(2), pages 171-183, March.
    14. Marzena Rostek, 2010. "Quantile Maximization in Decision Theory ," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 339-371.
    15. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    16. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Song, Bing & Zhang, Zhipeng & Qin, Yong & Liu, Xiang & Hu, Hao, 2022. "Quantitative analysis of freight train derailment severity with structured and unstructured data," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. Manon Costa & Sébastien Gadat, 2021. "Non-asymptotic study of a recursive superquantile estimation algorithm," Post-Print hal-03610477, HAL.
    3. Gadat, Sébastien & Costa, Manon, 2020. "Non asymptotic controls on a stochastic algorithm for superquantile approximation," TSE Working Papers 20-1149, Toulouse School of Economics (TSE).

    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. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
    2. Yu-Zhu Tian & Man-Lai Tang & Wai-Sum Chan & Mao-Zai Tian, 2021. "Bayesian bridge-randomized penalized quantile regression for ordinal longitudinal data, with application to firm’s bond ratings," Computational Statistics, Springer, vol. 36(2), pages 1289-1319, June.
    3. Yu, Dengdeng & Zhang, Li & Mizera, Ivan & Jiang, Bei & Kong, Linglong, 2019. "Sparse wavelet estimation in quantile regression with multiple functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 12-29.
    4. Tian, Yuzhu & Song, Xinyuan, 2020. "Bayesian bridge-randomized penalized quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. Guangrui Tang & Neng Fan, 2022. "A Survey of Solution Path Algorithms for Regression and Classification Models," Annals of Data Science, Springer, vol. 9(4), pages 749-789, August.
    6. 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.
    7. Dengluan Dai & Anmin Tang & Jinli Ye, 2023. "High-Dimensional Variable Selection for Quantile Regression Based on Variational Bayesian Method," Mathematics, MDPI, vol. 11(10), pages 1-22, May.
    8. Ioannis D. Vrontos & John Galakis & Ekaterini Panopoulou & Spyridon D. Vrontos, 2024. "Forecasting GDP growth: The economic impact of COVID‐19 pandemic," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(4), pages 1042-1086, July.
    9. Pfarrhofer, Michael, 2022. "Modeling tail risks of inflation using unobserved component quantile regressions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    10. Marfè, Roberto & Pénasse, Julien, 2024. "Measuring macroeconomic tail risk," Journal of Financial Economics, Elsevier, vol. 156(C).
    11. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.
    12. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    13. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    14. Salaheddine El Adlouni, 2018. "Quantile regression C-vine copula model for spatial extremes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(1), pages 299-317, October.
    15. Elisabeth Waldmann & Thomas Kneib & Yu Ryan Yu & Stefan Lang, 2012. "Bayesian semiparametric additive quantile regression," Working Papers 2012-06, Faculty of Economics and Statistics, Universität Innsbruck.
    16. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    17. Lane F. Burgette & Jerome P. Reiter, 2012. "Modeling Adverse Birth Outcomes via Confirmatory Factor Quantile Regression," Biometrics, The International Biometric Society, vol. 68(1), pages 92-100, March.
    18. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.
    19. Jiang, Liewen & Bondell, Howard D. & Wang, Huixia Judy, 2014. "Interquantile shrinkage and variable selection in quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 208-219.
    20. de Castro, Luciano & Galvao, Antonio F. & Montes-Rojas, Gabriel, 2020. "Quantile selection in non-linear GMM quantile models," Economics Letters, Elsevier, vol. 195(C).

    More about this item

    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:eee:reensy:v:201:y:2020:i:c:s0951832019300638. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.