THE ESTIMATION OF DISTRIBUTIONS UNDER A PARTICULAR RANDOM CENSORING

Abstract

Let X_1; X_2,…,X_N be i.i.d. random variables with distribution function F and censored by Y_1 Y_2…, Y_N. We can only observe (Z_t δ_t), i=1, 2,…, n and δ_i,i= n+1,…, N, where This model was proposed by Suzuki, K. (1985) and he discussed the case tnat X_t is a discrete random variable taking finite values. In this paper we discuss the case that X_t has a continuous distribution function F. We propose a estimator F of F and prove that N~(1/2)(F(t)-F(t)) converges to a Gussion process.