Physical Sciences and Mathematics Commons^™

Regression-Based Methods For Dynamic Treatment Regimes With Mismeasured Covariates Or Misclassified Response, Dan Liu

Electronic Thesis and Dissertation Repository

The statistical study of dynamic treatment regimes (DTRs) focuses on estimating sequential treatment decision rules tailored to patient-level information across multiple stages of intervention. Regression-based methods in DTR have been studied in the literature with a critical assumption that all the observed variables are precisely measured. However, this assumption is often violated in many applications. One example is the STAR*D study, in which the patient's depressive score is subject to measurement error. In this thesis, we explore problems in the context of DTR with measurement error or misclassification considered in the observed data.

The first project deals with covariate measurement …

An Analysis Of Weighted Least Squares Monte Carlo, Xiaotian Zhu

Electronic Thesis and Dissertation Repository

Since Longstaff and Schwartz [2001] brought the amazing Regression-based Monte Carlo (LSMC) method in pricing American options, it has received heated discussion. Based on the research done by Fabozzi et al. [2017] that applies the heteroscedasticity correction method to LSMC, we further extend the study by introducing the methods from Park [1966] and Harvey [1976]. Our work shows that for a single stock American Call option modelled by GBM with two exercise opportunities, WLSMC or IRLSMC provides better estimates in continuation value than LSMC. However, they do not lead to better exercise decisions and hence have little to no effect …

New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie

Electronic Thesis and Dissertation Repository

This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes.

The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In …

Early-Warning Alert Systems For Financial-Instability Detection: An Hmm-Driven Approach, Xing Gu

Electronic Thesis and Dissertation Repository

Regulators’ early intervention is crucial when the financial system is experiencing difficulties. Financial stability must be preserved to avert banks’ bailouts, which hugely drain government's financial resources. Detecting in advance periods of financial crisis entails the development and customisation of accurate and robust quantitative techniques. The goal of this thesis is to construct automated systems via the interplay of various mathematical and statistical methodologies to signal financial instability episodes in the near-term horizon. These signal alerts could provide regulatory bodies with the capacity to initiate appropriate response that will thwart or at least minimise the occurrence of a financial crisis. …

Statistical Applications To The Management Of Intensive Care And Step-Down Units, Yawo Mamoua Kobara

Electronic Thesis and Dissertation Repository

This thesis proposes three contributing manuscripts related to patient flow management, server decision-making, and ventilation time in the intensive care and step-down units system.

First, a Markov decision process (MDP) model with a Monte Carlo simulation was performed to compare two patient flow policies: prioritizing premature step-down and prioritizing rejection of patients when the intensive care unit is congested. The optimal decisions were obtained under the two strategies. The simulation results based on these optimal decisions show that a premature step-down strategy contributes to higher congestion downstream. Counter-intuitively, premature step-down should be discouraged, and patient rejection or divergence actions should …