Abstract
This paper studies the kernel assisted conditional Nelson-Aalen and Kaplan-Meier estimators. The presented results improve the existing ones in two aspects: (1) the asymptotic properties (uniform consistency, rate of convergence and almost sure iid representation) are extended to the entire support of the covariates by use of Müller-Wang boundary kernel; and (2) the order of the remainder terms in the iid representation is improved from (log n/(nhd))3/4 to log n/(nhd) thanks to the exponential inequality for U-statistics of order two. These results are useful for semiparametric estimation based on a first stage nonparametric estimation.
| Original language | English |
|---|---|
| Title of host publication | Recent Advances In Biostatistics |
| Subtitle of host publication | False Discovery Rates, Survival Analysis, And Related Topics |
| Publisher | World Scientific Publishing Co. |
| Pages | 61-86 |
| Number of pages | 26 |
| ISBN (Electronic) | 9789814329804 |
| State | Published - 1 Jan 2011 |