On estimation of partially linear transformation models

Wenbin Lu, Hao Helen Zhang

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We study a general class of partially linear transformation models, which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis. A new martingale-based estimating equation approach, consisting of both global and kernelweighted local estimation equations, is developed for estimating the parametric and nonparametric covariate effects in a unified manner. We show that with a proper choice of the kernel bandwidth parameter, one can obtain the consistent and asymptotically normal parameter estimates for the linear effects. Asymptotic properties of the estimated nonlinear effects are established as well.We further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness. To facilitate the implementation of the new procedure, an iterative algorithm is developed. Numerical examples are given to illustrate the finite-sample performance of the procedure. Supplementary materials are available online.

Original languageEnglish (US)
Pages (from-to)683-691
Number of pages9
JournalJournal of the American Statistical Association
Issue number490
StatePublished - Jun 2010


  • Estimating equations
  • Local polynomials
  • Martingale
  • Resampling

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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