TWO-STAGE SAMPLING SEQUENTIAL DENSITY ESTIMATION FROM CENSORED DATA

Letx₁,x₂,, …be a sequence of i. i. d. random oariables with distribution function F and density function f. The X_i are censored on the right by Y_i, where the Y_i are iid. random variables and independent of X_i. We only observe the sample Z_i=min（X_i,Y_i）,δ_i=I（X_i≤Y_i） The estimator f_n（$\hat{f}_n$） based on the Kaplan-Meier estimator is the kernel-type estimate of f from Z₁, …, Z_n. In this paper, we construct a fixed-width sequantial confidence interval based on f_n（$\hat{f}_n$） Some asymptotic properties are discussed, and we give an asymptotically efficient two-stage procedure.