ON THE UNIFORM CONSISTENCY OF THE KAPLAN-MEIER ESTIMATOR UNDER HEAVY CENSORING

摘要

Let X_i i.i.d. and Y_i i.i.d. be two sequences of random variables with unknown distribu- tion functions F(x) and G(y) respectively. X_i are censored by Y_i. In this paper we study the uni- form consistency of the Kaplan-Meier estimator under the case τ_F = sup(t:F(t) < 1) > τ_G = sup(t:G(t) < 1). The sufficient condition is discussed.