Smooth estimation of stochastically ordered survival functions

摘要: Let F and G be two survival functions. Sometimes it is known a prior that G (r)> F (r) for all r. In the one-sample case when F is known, the estimator. G.= max (G. F) of the survival function G. has been considered by many researchers in the literature. Here G, denotes the empirical survival function based on a sample of size n from the pop-ulation with survival function G. In the two-sample case when both F and G are unknown. the corresponding esti-mators are, G...= max (GF) and F...= min (GF).These estimators, typically. have jumps at the data points and there is naturally an interest in finding smooth estimators. The popular smoothing methods do not guarantee the stochastic ordering property in the resulting estimators. This paper presents an adaptation of the smoothing technique introduced in Chaubey and Sen| Statistics and Decisions 14. 1996|| and investigates the asymptotic properties of the resulting …