Some Large Sample Results for Nonparametric Estimators Under the Competing Risks Case
 
                 
                
                    
                                        
                    - 
Graphical Abstract
 
                                        
                    - 
Abstract
    In this paper, we consider the PL-type estimator of survival curves and its consistency and weak convergence under tile competing risks case. In addition, we propose a simple estimator for the immune proportion in a population, which is shown to be consistent and the asymptotic normality of the estimator is also obtained.
 
                                        
                    - 
                        
                     
                    
                    
                                        
                    -