IDEAS home Printed from
   My bibliography  Save this article

Maximum likelihood estimation for conditional distribution single-index models under censoring


  • Strzalkowska-Kominiak, Ewa
  • Cao, Ricardo


A new likelihood approach is proposed for the problem of semiparametric estimation of a conditional distribution or density under censoring. Consistency and asymptotic normality for two versions of the maximum likelihood estimator of the parameter vector in the single index model are proved. The single-index model considered can be seen as a useful tool for credit scoring and estimation of the default probability in credit risk. A data-driven bandwidth selection procedure is proposed. It allows to choose the smoothing parameter involved in our approach. The finite sample performance of the estimators has been studied by simulations, where the new method has been compared with the method proposed by Bouaziz and Lopez (2010) [1]. To the best of our knowledge this is the only existing competitor in this context. The simulation study shows the good behavior of the proposed method.

Suggested Citation

  • Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.
  • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:74-98
    DOI: 10.1016/j.jmva.2012.07.012

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    1. Lu, Xuewen & Cheng, Tsung-Lin, 2007. "Randomly censored partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1895-1922, November.
    2. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    3. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
    4. Lu, Xuewen, 2010. "Asymptotic distributions of two "synthetic data" estimators for censored single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 999-1015, April.
    5. Michael McAleer & Bernardo da Veiga, 2008. "Single-index and portfolio models for forecasting value-at-risk thresholds," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(3), pages 217-235.
    6. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    7. Jiti Gao & Hua Liang, 1997. "Statistical Inference in Single-Index and Partially Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 493-517, September.
    8. Zhang, Riquan & Huang, Zhensheng & Lv, Yazhao, 2010. "Statistical inference for the index parameter in single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 1026-1041, April.
    9. Gascuel, O. & Caraux, G., 1992. "Bounds on expectations of order statistics via extremal dependences," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 143-148, September.
    10. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    11. Okolewski, Andrzej & Rychlik, Tomasz, 2001. "Sharp distribution-free bounds on the bias in estimating quantiles via order statistics," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 207-213, April.
    12. Delecroix, Michel & Härdle, Wolfgang & Hristache, Marian, 2003. "Efficient estimation in conditional single-index regression," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 213-226, August.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. repec:spr:testjl:v:27:y:2018:i:2:d:10.1007_s11749-017-0546-2 is not listed on IDEAS
    2. Luís Meira-Machado & Jacobo Uña-Álvarez & Somnath Datta, 2015. "Nonparametric estimation of conditional transition probabilities in a non-Markov illness-death model," Computational Statistics, Springer, vol. 30(2), pages 377-397, June.
    3. Catalina Bolancé & Ricardo Cao & Montserrat Guillen, 2018. "“Flexible maximum conditional likelihood estimation for single-index models to predict accident severity with telematics data”," IREA Working Papers 201829, University of Barcelona, Research Institute of Applied Economics, revised Dec 2018.
    4. repec:spr:aistmt:v:70:y:2018:i:3:d:10.1007_s10463-017-0600-6 is not listed on IDEAS
    5. Ewa Strzalkowska-Kominiak & Ricardo Cao, 2014. "Beran-based approach for single-index models under censoring," Computational Statistics, Springer, vol. 29(5), pages 1243-1261, October.


    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:jmvana:v:114:y:2013:i:c:p:74-98. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.