Sequential estimarion of functionals of the survival curve under random censorship

Abstract

Sequential point and interval estimation procedures for functionals of the survival curve F of the form ∫ψdF and ∫Fdψ with censored data are considered. The sequential point estimatior, procedure is shown to be risk efficient and asymptotically normal as c, cost per unit observation, tends to zero. For the interval estimation problem, the sequential procedure is shown to be consistent and efficient as the width of the confidence interval decreases to zero. In both estimation problems, the asymptotic distribution of the underlying stopping rule is obtained.

Keywords:

• product-limit estimator
• stopping time
• risk efficiency
• consistency
• efficiency