Tan, Fang (2006) Nonparametric maximum likelihood estimation in cure-rate models based on uncensored and censored data. Masters thesis, Concordia University.
MR14234.pdf - Accepted Version
In this thesis, we shall attempt to give the NPMLE of the event time distribution and cure-rate based on different types of uncensored and censored data. Cure-mixture model and hidden model are used extensively. We address the non-estimability of the cure-rate when no cures are actually observed, in the uncensored case and some important censoring models. A proof is also given for the almost sure convergence of [Special characters omitted.] F ( x ) to (1 - s), where [Special characters omitted.] F ( x ) is the supremum of the MLE of the underlying distribution function, and s is the true underlying cure-rate, for random censoring and interval censoring (case-1). We describe and illustrate the "max-min formula" derived by Groeneboom and Wellner (1992) for interval censoring (case-1), then modify it to get the MLE of the cure-rate under a cure-mixture model, when some cures are observed. We perform a simulation study to give some numerical results as well. Finally, we discuss a probable approach to find the NPMLE in interval censoring (case-2), as a problem for further research.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Thesis (Masters)|
|Pagination:||vii, 52 leaves ; 29 cm.|
|Degree Name:||M. Sc.|
|Program:||Mathematics and Statistics|
|Thesis Supervisor(s):||Sen, Arusharka|
|Deposited By:||Concordia University Libraries|
|Deposited On:||18 Aug 2011 18:38|
|Last Modified:||05 Nov 2016 01:12|
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