Abstract
Statistical conceptions, methods and models are used in a wide variety of research fields such as clinical trials, economics, and operation research. They are important in data analysis and decision making. This dissertation separately addresses two challenging problems in suvival analysis and operation research.In the first part of this dissertation, we consider the estimation problem in the analysis of incomplete data. More specifically, we are interested in the chanllenges of analysing length-biased data with right censoring and missing covariates in additive hazard model. Two approaches are proposed for analysing the aforementioned two types of incomplete datasets. We then compare the two estimators proposed by our methods to other approaches and show that our estimators are consistent and asymptotically normal under milder conditions, in both theory and practice. In addition, we also derive the strong representations and the rates of approximation of the proposed estimators.
In the second part, we turn to the problem of input uncertainty reduction in stochastic simulations. Input uncertainty is an aspect of simulation model risk that arises when the driving input distributions are derived or “fit” to real-world, historical data. Although there has been significant progress in quantifying and hedging against input uncertainty, there has been no direct attempt to reduce it. One important contribution of this thesis is its proof that frequentist model averaging can effectively create input models that better represent the true, unknown input distributions, thereby reducing model risk. Input model averaging builds from standard input modelling practice, and requires no change in how the simulation is executed or any follow-up experiments. We provide theoretical and empirical support for our approach.
| Date of Award | 16 Aug 2017 |
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| Original language | English |
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| Supervisor | Tze-Kin Alan WAN (Supervisor) & Yong Zhou (External Supervisor) |