THE STRONG LAW FOR THE P-L ESTIMATE IN THE LEFT TRUNCATED AND RIGHT CENSORED MODEL (I)  

作　　者：HE SHUYUAN 

机构地区：[1]不详

出　　处：《Chinese Annals of Mathematics,Series B》1998年第3期341-348,共8页数学年刊(B辑英文版)

摘　　要：For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.

关 键 词：Left truncation and right censoring Product-limit estimate Strong law of large numbers Reversed supermartingale 

分 类 号：O211.4[理学—概率论与数理统计] O211.5[理学—数学]