IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v43y2016i7p1240-1252.html
   My bibliography  Save this article

A class of finite mixture of quantile regressions with its applications

Author

Listed:
  • Yuzhu Tian
  • Manlai Tang
  • Maozai Tian

Abstract

Mixture of linear regression models provide a popular treatment for modeling nonlinear regression relationship. The traditional estimation of mixture of regression models is based on Gaussian error assumption. It is well known that such assumption is sensitive to outliers and extreme values. To overcome this issue, a new class of finite mixture of quantile regressions (FMQR) is proposed in this article. Compared with the existing Gaussian mixture regression models, the proposed FMQR model can provide a complete specification on the conditional distribution of response variable for each component. From the likelihood point of view, the FMQR model is equivalent to the finite mixture of regression models based on errors following asymmetric Laplace distribution (ALD), which can be regarded as an extension to the traditional mixture of regression models with normal error terms. An EM algorithm is proposed to obtain the parameter estimates of the FMQR model by combining a hierarchical representation of the ALD. Finally, the iterated weighted least square estimation for each mixture component of the FMQR model is derived. Simulation studies are conducted to illustrate the finite sample performance of the estimation procedure. Analysis of an aphid data set is used to illustrate our methodologies.

Suggested Citation

  • Yuzhu Tian & Manlai Tang & Maozai Tian, 2016. "A class of finite mixture of quantile regressions with its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1240-1252, July.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:7:p:1240-1252
    DOI: 10.1080/02664763.2015.1094035
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2015.1094035
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2015.1094035?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. Young, D.S. & Hunter, D.R., 2010. "Mixtures of regressions with predictor-dependent mixing proportions," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2253-2266, October.
    2. D. Oakes, 1999. "Direct calculation of the information matrix via the EM," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 479-482, April.
    3. T. Rolf Turner, 2000. "Estimating the propagation rate of a viral infection of potato plants via mixtures of regressions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(3), pages 371-384.
    4. Mian Huang & Weixin Yao, 2012. "Mixture of Regression Models With Varying Mixing Proportions: A Semiparametric Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 711-724, June.
    5. Pierre Vandekerkhove, 2013. "Estimation of a semiparametric mixture of regressions model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 181-208, March.
    6. Bai, Xiuqin & Yao, Weixin & Boyer, John E., 2012. "Robust fitting of mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2347-2359.
    7. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    8. Song, Weixing & Yao, Weixin & Xing, Yanru, 2014. "Robust mixture regression model fitting by Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 128-137.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. Hong‐Tu Zhu & Heping Zhang, 2004. "Hypothesis testing in mixture regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 3-16, February.
    11. Bengt Muthén & Tihomir Asparouhov, 2009. "Multilevel regression mixture analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 639-657, June.
    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. Ang Shan & Fengkai Yang, 2021. "Bayesian Inference for Finite Mixture Regression Model Based on Non-Iterative Algorithm," Mathematics, MDPI, vol. 9(6), pages 1-13, March.

    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. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    2. Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    3. Atefeh Zarei & Zahra Khodadadi & Mohsen Maleki & Karim Zare, 2023. "Robust mixture regression modeling based on two-piece scale mixtures of normal distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 181-210, March.
    4. Yuzhu Tian & Manlai Tang & Yanchao Zang & Maozai Tian, 2018. "Quantile regression for linear models with autoregressive errors using EM algorithm," Computational Statistics, Springer, vol. 33(4), pages 1605-1625, December.
    5. Wang, Shangshan & Xiang, Liming, 2017. "Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 136-154.
    6. Marco Berrettini & Giuliano Galimberti & Saverio Ranciati, 2023. "Semiparametric finite mixture of regression models with Bayesian P-splines," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 745-775, September.
    7. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2016. "Estimation of linear composite quantile regression using EM algorithm," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 183-191.
    8. Akosah, Nana Kwame & Alagidede, Imhotep Paul & Schaling, Eric, 2020. "Testing for asymmetry in monetary policy rule for small-open developing economies: Multiscale Bayesian quantile evidence from Ghana," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).
    9. Paul Hewson & Keming Yu, 2008. "Quantile regression for binary performance indicators," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 401-418, September.
    10. Chen, Cathy W.S. & Gerlach, Richard & Hwang, Bruce B.K. & McAleer, Michael, 2012. "Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range," International Journal of Forecasting, Elsevier, vol. 28(3), pages 557-574.
    11. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    12. Michel Lubrano & Abdoul Aziz Junior Ndoye, 2014. "Bayesian Unconditional Quantile Regression: An Analysis of Recent Expansions in Wage Structure and Earnings Inequality in the US 1992–2009," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(2), pages 129-153, May.
    13. Tsionas, Mike G., 2020. "Quantile Stochastic Frontiers," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1177-1184.
    14. Pfarrhofer, Michael, 2022. "Modeling tail risks of inflation using unobserved component quantile regressions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    15. Wu Wang & Zhongyi Zhu, 2017. "Conditional empirical likelihood for quantile regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 1-16, January.
    16. Marco Bottone & Lea Petrella & Mauro Bernardi, 2021. "Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1079-1107, September.
    17. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    18. Zijian Zeng & Meng Li, 2020. "Bayesian Median Autoregression for Robust Time Series Forecasting," Papers 2001.01116, arXiv.org, revised Dec 2020.
    19. Alexander März & Nadja Klein & Thomas Kneib & Oliver Musshoff, 2016. "Analysing farmland rental rates using Bayesian geoadditive quantile regression," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 43(4), pages 663-698.
    20. Yingying Hu & Huixia Judy Wang & Xuming He & Jianhua Guo, 2021. "Bayesian joint-quantile regression," Computational Statistics, Springer, vol. 36(3), pages 2033-2053, September.

    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:taf:japsta:v:43:y:2016:i:7:p:1240-1252. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.