|
|
| |
| THE STRONG LAW FOR THE P-L ESTIMATE IN THE LEFT TRUNCATED AND RIGHT CENSORED MODEL (I) |
| |
Citation： |
He Shuyuan.THE STRONG LAW FOR THE P-L ESTIMATE IN THE LEFT TRUNCATED AND RIGHT CENSORED MODEL (I)[J].Chinese Annals of Mathematics B,1998,19(3):341~348 |
| Page view： 960
Net amount： 753 |
Authors： |
He Shuyuan; |
Foundation： |
Project supported by the National Natural Science
Foundation of China. |
|
|
| Abstract： |
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 $\Lambda_n$ and the product-limit estimate $F_n$ are
strong consistent. For any nonnegative measurable $\phi$, the almost sure
convergences of $\int \phi \,d\Lambda_n$ and $\int \phi \,dF_n$ to the true
values $\int \phi \,d\Lambda$ and $\int \phi \,dF$ respectively are obtained.
The strong consistency of the estimator for the truncation probability is
proved. |
Keywords： |
Left truncation and right censoring, Product-limit estimate,
Strong law of large numbers, Reversed supermartingale |
Classification： |
62G05, 60F15 |
|
|
Download PDF Full-Text
|
|
|
|
