Abstract
For censored response variable against projected co-variable, a generalized linear model with an unknown link function can cover almost all existing models under censorship. Its special cases include the accelerated failure time model with censored data. Such a model in the uncensored case is called the single-index model in econometrics. In this paper, we systematically study the asymptotic properties. We derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter. We also obtain the optimal convergence rate of an estimator of the unknown link function in the model.
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Wang, Y., He, S., Zhu, L. et al. Asymptotics for a censored generalized linear model with unknown link function. Probab. Theory Relat. Fields 138, 235–267 (2007). https://doi.org/10.1007/s00440-006-0022-5
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DOI: https://doi.org/10.1007/s00440-006-0022-5
Keywords
- Central limit theorem
- Projection pursuit regression
- Random censorship
- Generalized linear model
- Unknown link
Mathematics Subject Classification (2000)
- Primary 62H99
- Secondary 62H05