IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v8y2012i1n10.html
   My bibliography  Save this article

Smoothness Selection for Penalized Quantile Regression Splines

Author

Listed:
  • Reiss Philip T.

    (New York University and Nathan Kline Institute)

  • Huang Lei

    (Johns Hopkins University)

Abstract

Modern data-rich analyses may call for fitting a large number of nonparametric quantile regressions. For example, growth charts may be constructed for each of a collection of variables, to identify those for which individuals with a disorder tend to fall in the tails of their age-specific distribution; such variables might serve as developmental biomarkers. When such a large set of analyses are carried out by penalized spline smoothing, reliable automatic selection of the smoothing parameter is particularly important. We show that two popular methods for smoothness selection may tend to overfit when estimating extreme quantiles as a smooth function of a predictor such as age; and that improved results can be obtained by multifold cross-validation or by a novel likelihood approach. A simulation study, and an application to a functional magnetic resonance imaging data set, demonstrate the favorable performance of our methods.

Suggested Citation

  • Reiss Philip T. & Huang Lei, 2012. "Smoothness Selection for Penalized Quantile Regression Splines," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-27, May.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:1:n:10
    DOI: 10.1515/1557-4679.1381
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/1557-4679.1381
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/1557-4679.1381?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. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    3. Bosch, Ronald J. & Ye, Yinyu & Woodworth, George G., 1995. "A convergent algorithm for quantile regression with smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 613-630, June.
    4. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    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. Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    8. Yue, Yu Ryan & Rue, Håvard, 2011. "Bayesian inference for additive mixed quantile regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 84-96, January.
    9. Philip T. Reiss & R. Todd Ogden, 2009. "Smoothing parameter selection for a class of semiparametric linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 505-523, April.
    10. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    11. Krivobokova, Tatyana & Kauermann, Goran, 2007. "A Note on Penalized Spline Smoothing With Correlated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1328-1337, December.
    12. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    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. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    2. Zhang, Likun & Castillo, Enrique del & Berglund, Andrew J. & Tingley, Martin P. & Govind, Nirmal, 2020. "Computing confidence intervals from massive data via penalized quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Yaeji Lim & Hee-Seok Oh, 2015. "Simultaneous confidence interval for quantile regression," Computational Statistics, Springer, vol. 30(2), pages 345-358, June.

    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. Lauren N. Berry & Nathaniel E. Helwig, 2021. "Cross-Validation, Information Theory, or Maximum Likelihood? A Comparison of Tuning Methods for Penalized Splines," Stats, MDPI, vol. 4(3), pages 1-24, September.
    2. Andrada Ivanescu & Ana-Maria Staicu & Fabian Scheipl & Sonja Greven, 2015. "Penalized function-on-function regression," Computational Statistics, Springer, vol. 30(2), pages 539-568, June.
    3. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    4. Roel Verbelen & Katrien Antonio & Gerda Claeskens, 2018. "Unravelling the predictive power of telematics data in car insurance pricing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1275-1304, November.
    5. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.
    6. Rodrigues, T. & Dortet-Bernadet, J.-L. & Fan, Y., 2019. "Simultaneous fitting of Bayesian penalised quantile splines," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 93-109.
    7. Philip T. Reiss & Lei Huang & Pei‐Shien Wu & Huaihou Chen & Stan Colcombe, 2017. "Pointwise influence matrices for functional‐response regression," Biometrics, The International Biometric Society, vol. 73(4), pages 1092-1101, December.
    8. Arthur Charpentier & Emmanuel Flachaire & Antoine Ly, 2017. "Econom\'etrie et Machine Learning," Papers 1708.06992, arXiv.org, revised Mar 2018.
    9. Michael Wegener & Göran Kauermann, 2017. "Forecasting in nonlinear univariate time series using penalized splines," Statistical Papers, Springer, vol. 58(3), pages 557-576, September.
    10. Basile, Roberto & Durbán, María & Mínguez, Román & María Montero, Jose & Mur, Jesús, 2014. "Modeling regional economic dynamics: Spatial dependence, spatial heterogeneity and nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 229-245.
    11. Daniel Melser, 2017. "Residential Real Estate, Risk, Return and Home Characteristics: Evidence from Sydney 2002-14," ERES eres2017_296, European Real Estate Society (ERES).
    12. Feng, Yuanhua & Härdle, Wolfgang Karl, 2020. "A data-driven P-spline smoother and the P-Spline-GARCH models," IRTG 1792 Discussion Papers 2020-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    13. Arthur Charpentier & Emmanuel Flachaire & Antoine Ly, 2018. "Économétrie & Machine Learning," Working Papers hal-01568851, HAL.
    14. Rasheed A. Adeyemi & Temesgen Zewotir & Shaun Ramroop, 2016. "Semiparametric Multinomial Ordinal Model to Analyze Spatial Patterns of Child Birth Weight in Nigeria," IJERPH, MDPI, vol. 13(11), pages 1-22, November.
    15. Gressani, Oswaldo & Lambert, Philippe, 2021. "Laplace approximations for fast Bayesian inference in generalized additive models based on P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    16. Roberto Basile, 2014. "Regional productivity growth in Europe: a Schumpeterian perspective," Gecomplexity Discussion Paper Series 1, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Nov 2014.
    17. Christian Schellhase & Göran Kauermann, 2012. "Density estimation and comparison with a penalized mixture approach," Computational Statistics, Springer, vol. 27(4), pages 757-777, December.
    18. Marta Karas & Damian Brzyski & Mario Dzemidzic & Joaquín Goñi & David A. Kareken & Timothy W. Randolph & Jaroslaw Harezlak, 2019. "Brain Connectivity-Informed Regularization Methods for Regression," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 47-90, April.
    19. Gertheiss, Jan & Goldsmith, Jeff & Staicu, Ana-Maria, 2017. "A note on modeling sparse exponential-family functional response curves," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 46-52.
    20. Zanin, Luca, 2023. "A flexible estimation of sectoral portfolio exposure to climate transition risks in the European stock market," Journal of Behavioral and Experimental Finance, Elsevier, vol. 39(C).

    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:bpj:ijbist:v:8:y:2012:i:1:n:10. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.