Date of Award
Mathematics and Statistics
Nkurunziza, Severien (Economics, Mathematics, and Statistics)
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This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Survival analysis is a branch of statistics which deals with the analysis of time to event (or in general event history). In particular, regression models that relate event occurrence rates to predictor variables are quite common in the medical field. One such regression model is the Aalen's nonparametric additive model in which the regression coefficients are assumed to be unspecified functions of time. In this project we consider estimation of Aalen's nonparametric regression coefficients when some uncertain prior information is available about these coefficients. More precisely, we combine unrestricted estimators and estimators that are restricted by a linear hypothesis (prior information) and produce James-Stein-type of shrinkage estimators. We develop the asymptotic joint distribution of such restricted and unrestricted estimators and use it for studying the relative performance of the proposed estimators via their asymptotic distributional biases and risks. We conduct Monte Carlo simulations to examine relative performance of the estimators in small samples and we illustrate the methodology by using a real data on the survival of primary biliary cirrhosis patients.
Tomanelli, Katrina, "Shrinkage Estimation for Aalen's Additive Model" (2012). Electronic Theses and Dissertations. 353.