Median Regression For Censoring Nonlinear Model

Survival Analysis, which can deal with censored data confronted in daily life perfectly, is one of the most popular fields in Statistics nowadays. Meanwhile, it has revealed some more complicated academic problems and accelerates the development of Statistics.Median regression for nonlinear model with randomly right censored data is studied in this paper. L₁ inference, which is often used in linear model with complete observations, is extended to median regression for nonlinear model with incomplete observations in chapter 1. A semiparametric procedure is proposed to estimate the parameter in nonlinear median regression model with randomly right censored data. The strong consistency and asymptotic normality of the estimator are also obtained.In chapter 2, empirical likelihood is developed to median regression for nonlinear model with randomly right censored data. The asymptotic distribution of empirical likelihood ratio function is obtained. And it is weighted chi-square distribution but standard chi-squared. This approach provides an admirable tool to construct confidence regions of regression parameter.