On Estimating Survival Functions Under Stochastic Order

Let H̄ , Ḡ, and H̄ be survival functions satisfying the constraint F̄ ≤ H̄≤Ḡ. Lee, Yan, and Shi (1999) had developed an algorithm to estimate the survival function H̄ when F̄ and Ḡ are known. However, lacking a closed form of the estimator makes the investigations of the properties of the estimators difficult. In this paper, we propose alternative estimators for H̄ in the case where F̄ and Ḡ are known. However, lacking a closed form of the estimator makes the investigations of the properties of the estimator difficult. In this paper we propose alternative estimators for H̄ in the case where F̄ and Ḡ are known and in the case where they are unknown. The estimators are proved to be strongly uniformly consistent in both cases: the formulas for the bias and the mean squared error (MSE) are also derived. In the simulations the MSE of our estimators, when F̄and Ḡare known, are uniformly better thn that of Lee, Yan, and Shi when the sample size is small (30): when the sample size is large, further investigation is needed.