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

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  • Strzalkowska-Kominiak, Ewa
  • Cao, Ricardo

Abstract

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
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    References listed on IDEAS

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    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.
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    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.

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