Versatile estimation in censored single-index hazards regression

  • Chin-Tsang Chiang
  • Shao-Hsuan Wang
  • Ming-Yueh Huang


One attractive advantage of the presented single-index hazards regression is that it can take into account possibly time-dependent covariates. In such a model formulation, the main theme of this research is to develop a theoretically valid and practically feasible estimation procedure for the index coefficients and the induced survival function. In particular, compared with the existing pseudo-likelihood approaches, our one proposes an automatic bandwidth selection and suppresses an influence of outliers. By making an effective use of the considered versatile survival process, we further reduce a substantial finite-sample bias in the Chambless-Diao type estimator of the most popular time-dependent accuracy summary. The asymptotic properties of estimators and data-driven bandwidths are also established under some suitable conditions. It is found in simulations that the proposed estimators and inference procedures exhibit quite satisfactory performances. Moreover, the general applicability of our methodology is illustrated by two empirical data.


Accuracy measure Conditional survival function Cross-validation Kaplan–Meier estimator Pseudo-integrated least squares estimator Pseudo-maximum likelihood estimator Single-index hazards model U-statistic 



The research of the first author was partially supported by the National Science Council Grants 99-2118-M-002-003- and 100-2118-M-002-005-MY2 (Taiwan). We would also like to thank the associate editor and a reviewer for some constructive comments on this paper.

Supplementary material

10463_2017_600_MOESM1_ESM.pdf (178 kb)
Supplementary material 1 (pdf 178 KB)


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  • Chin-Tsang Chiang
    • 1
  • Shao-Hsuan Wang
    • 1
  • Ming-Yueh Huang
    • 1
  1. 1.Institute of Applied Mathematical SciencesNational Taiwan UniversityTaipeiTaiwan, ROC

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