TY - JOUR
T1 - On estimation of partially linear transformation models
AU - Lu, Wenbin
AU - Zhang, Hao Helen
N1 - Funding Information:
Wenbin Lu is Associate Professor (E-mail: [email protected]) and Hao Helen Zhang is Associate Professor (E-mail: [email protected]), Department of Statistics, North Carolina State University, Raleigh, NC 27695. The authors thank the editor, an associate editor, and two referees for their constructive comments and suggestions, and Professor Kani Chen for inspiring discussions on the consistency of the proposed estimators. This research was partially supported by the NSF awards DMS-0504269 and DMS-0645293, and the NIH awards R01 CA-085848 and R01 CA-140632.
PY - 2010/6
Y1 - 2010/6
N2 - 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.
AB - 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.
KW - Estimating equations
KW - Local polynomials
KW - Martingale
KW - Resampling
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U2 - 10.1198/jasa.2010.tm09302
DO - 10.1198/jasa.2010.tm09302
M3 - Article
AN - SCOPUS:78649427504
SN - 0162-1459
VL - 105
SP - 683
EP - 691
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 490
ER -