Date of Award
12-1-2018
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Gerhard Dikta
Second Advisor
Jay H Beder
Third Advisor
Jugal Ghorai
Committee Members
Vytaras Brazauskas, Chao Zhu
Keywords
Kaplan-Meier estimator, reverse supermartingale, semi-parametric, SLLN, survival analysis
Abstract
We introduce a semi-parametric U-statistics estimator for randomly right censored data. We will study the strong law of large numbers for this estimator under proper assumptions about the conditional expectation of the censoring indicator with re- spect to the observed life times. Moreover we will conduct simulation studies, where the semi-parametric estimator is compared to a U-statistic based on the Kaplan- Meier product limit estimator in terms of bias, variance and mean squared error, under different censoring models.
Recommended Citation
Höft, Jan, "The Strong Law of Large Numbers for U-Statistics under Random Censorship" (2018). Theses and Dissertations. 1968.
https://dc.uwm.edu/etd/1968