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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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    9. 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.
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    Cited by:

    1. Weiyu Li & Valentin Patilea, 2018. "A dimension reduction approach for conditional Kaplan–Meier estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 295-315, June.
    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. Chin-Tsang Chiang & Shao-Hsuan Wang & Ming-Yueh Huang, 2018. "Versatile estimation in censored single-index hazards regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 523-551, June.
    5. Rebeca Peláez & Ricardo Cao & Juan M. Vilar, 2022. "Bootstrap Bandwidth Selection and Confidence Regions for Double Smoothed Default Probability Estimation," Mathematics, MDPI, vol. 10(9), pages 1-25, May.
    6. 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.
    7. Ricardo Cao, 2019. "Comments on: Data science, big data and statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 664-670, September.

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