Asymptotics for a censored generalized linear model with unknown link function

Yanhua Wang, Shuyuan He, Lixing ZHU*, Kam C. Yuen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)235-267
Number of pages33
JournalProbability Theory and Related Fields
Volume138
Issue number1-2
DOIs
Publication statusPublished - 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

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