Mathematical Sciences: Semiparametric Models & Estimation of Survival Functions

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The two aspects of this research focus on semiparametric regression modeling and the properties of estimators and the comparative merits of different approaches. In the context of survival function analysis, the estimation problem focuses on the information in the censoring distribution and/or the observed censoring times. In the industrial context, the problem focuses on describing the behavior of the bootstrap methodology as used in smoothing and in determining conditions under which this is the superior methodology. Situations in which statistical models or functions can be described only partially in terms of identified factors or attributes occur widely. This project considers applications to data from medical trials and, separately, from industrial experimentation. When known features only specify part of the model, the unexplained part can be described in a number of different ways. This proposal seeks to identify the conditions which make each particular choice of methodology are sufficiently superior to make its use important.