Asymptotic distributions of two "synthetic data" estimators for censored single-index models

作者：Lu Xuewen^*

来源：Journal of Multivariate Analysis, 2010, 101(4): 999-1015.

DOI：10.1016/j.jmva.2009.09.001

• Accelerated failure time model
• Asymptotic normality
• rMAVE
• rOPG
• Random censoring
• Single-index model
• Synthetic data

The censored single-index model provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored and the link function is unknown. It presents a technique for "dimension reduction" in semiparametric censored regression models and generalizes the existing accelerated failure time models for survival analysis. This paper proposes two methods for estimation of single-index models with randomly censored samples. We first transform the censored data into synthetic data or pseudo-responses unbiasedly, then obtain estimates of the index coefficients by the rOPG or WAVE procedures of Xia (2006) [1]. Finally, we estimate the unknown nonparametric link function using techniques for univariate censored nonparametric regression. The estimators for the index coefficients are shown to be root-n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodologies.

• 出版日期2010-4