Abstract
Absfract: In this note the exact bias and variance functions of the nonparametric NelsonAalen estimator (NAE) of the cumulative hazard function (/lF) are compared with approximations provided by asymptotic theory under the Koziol-Green (KG) model of random censorship. It is found that for small sample sizes (ns30) the asymptotic approximations are very misleading when inferences are to be made on the tails of the cumulative hazard function and/or in the presence of a high degree of censoring. To ascertain the efficiency of the NAE under the KG model, a model-dependent estimator of /1, is obtained, and the exact and asymptotic efficiencies of the NAE relative to this estimator are derived. It is found that the NAE is always less efficient than this estimator under the KG model, and its asymptotic efficiency can be as low as the probability of an uncensored observation on both tails of nF. AMS Subject C~assificationt Primary 62N05; secondary 62F11,62F12
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
