THE ESTIMATION OF DISTRIBUTIONS UNDER A PARTICULAR RANDOM CENSORING

Let X₁, X₂,…,X_N be i.i.d. random variables with distribution function F and censored by Y₁, Y₂…, Y_N. We can only observe （Z_t, δ_t）,i=1, 2,…, n and δ_i,i=n+1,…, N, where Z_i=\min \left(X_i, Y_i\right), \delta_i=I\left(X_i \leqslant Y_i\right)= \begincases1 & X_iY_i\endcases,This model was proposed by Suzuki, K. （1985） and he discussed the case tnat X_i is a discrete random variable taking finite values. In this paper we discuss the case that X_i has a continuous distribution function F. We propose a estimator \hatF of F and prove that √N（\hatF(t)-F（t）） converges to a Gussion process.