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.
Original language | English |
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Pages (from-to) | 235-267 |
Number of pages | 33 |
Journal | Probability Theory and Related Fields |
Volume | 138 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - May 2007 |
Scopus Subject Areas
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty
User-Defined Keywords
- Central limit theorem
- Generalized linear model
- Projection pursuit regression
- Random censorship
- Unknown link