删失数据非线性回归模型的广义M估计

GENERALIZED M-ESTIMATION FOR NONLINEAR CENSORED REGRESSION

加速失效模型(AFT模型)是研究失效时间和协变量间相互关系的一类重要模型.在标准的AFT模型中,假设对数变换后的生存时间与协变量间是线性关系,本文将线性关系扩展到非线性,在广义M估计的目标函数中使用Kaplan-Meier权,提出右删失数据非线性回归模型的加权广义M估计.我们还得到了广义M估计的渐近性和相合性,并且通过模拟研究验证了该方法在有限样本情形下估计效果良好.

Accelerated failure time model is an important regression tool to study association between failure time and co^variates. In standard accelerated lifetime model, log lifetime is a linear function of co- variable vector. This model is now extended to admit general nonlinear functional relationships. We propose a robust weighted generalized M-estimation for nonlinear regression with right-censored data using the Kaplan- Meier weights in the generalized M type objective function to estimate regression coefficients and scale parameter simultaneously. Asymptotic properties including the root-n consistency and asymptotic normality are established for the resulting estimator under suitable conditions. Simulations suggest that the proposed estimator has good finite sample performance in comparison with existing robust estimators.