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.
|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.|
|Number of pages||26|
|State||Published - 1 Jan 2011|