Statistical Models Commons^™

Parameter Estimation For Normally Distributed Grouped Data And Clustering Single-Cell Rna Sequencing Data Via The Expectation-Maximization Algorithm, Zahra Aghahosseinalishirazi

Electronic Thesis and Dissertation Repository

The Expectation-Maximization (EM) algorithm is an iterative algorithm for finding the maximum likelihood estimates in problems involving missing data or latent variables. The EM algorithm can be applied to problems consisting of evidently incomplete data or missingness situations, such as truncated distributions, censored or grouped observations, and also to problems in which the missingness of the data is not natural or evident, such as mixed-effects models, mixture models, log-linear models, and latent variables. In Chapter 2 of this thesis, we apply the EM algorithm to grouped data, a problem in which incomplete data are evident. Nowadays, data confidentiality is of …

Modelling Long-Term Security Returns, Xinghan Zhu

Electronic Thesis and Dissertation Repository

This research focuses on the concerns of Canadian investors regarding portfolio diversification and preparedness for unexpected risks in retirement planning. It models market crashes and two main financial instruments as independent components to simulate clients’ portfolios. Initially exploring single distributions on mutual funds such as Laplace and t distributions, the research finds limited success. Instead, a normal-Weibull spliced distribution is introduced to model log returns. The Geometric Brownian Motion (GBM) model is employed to predict and evaluate returns on common stocks using the Maximum Likelihood Estimator (MLE), assuming that daily log returns follow a normal distribution. Additionally, the Merton Jump …

Addressing The Impact Of Time-Dependent Social Groupings On Animal Survival And Recapture Rates In Mark-Recapture Studies, Alexandru M. Draghici

Electronic Thesis and Dissertation Repository

Mark-recapture (MR) models typically assume that individuals under study have independent survival and recapture outcomes. One such model of interest is known as the Cormack-Jolly-Seber (CJS) model. In this dissertation, we conduct three major research projects focused on studying the impact of violating the independence assumption in MR models along with presenting extensions which relax the independence assumption. In the first project, we conduct a simulation study to address the impact of failing to account for pair-bonded animals having correlated recapture and survival fates on the CJS model. We examined the impact of correlation on the likelihood ratio test (LRT), …

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 …

Compound Sums, Their Distributions, And Actuarial Pricing, Ang Li

Electronic Thesis and Dissertation Repository

Compound risk models are widely used in insurance companies to mathematically describe their aggregate amount of losses during certain time period. However, evaluation of the distribution of compound random variables and the computation of the relevant risk measures are non-trivial. Therefore, the main purpose of this thesis is to study the bounds and simulation methods for both univariate and multivariate compound distributions. The premium setting principles related to dependent multivariate compound distributions are studied. .

In the first part of this thesis, we consider the upper and lower bounds of the tail of bivariate compound distributions. Our results extend those …

On The Estimation Of Heston-Nandi Garch Using Returns And/Or Options: A Simulation-Based Approach, Xize Ye

Electronic Thesis and Dissertation Repository

In this thesis, the Heston-Nandi GARCH(1,1) (henceforth, HN-GARCH) option pricing model is fitted via 4 maximum likelihood-based estimation and calibration approaches using simulated returns and/or options. The purpose is to examine the benefits of the joint estimation using both returns and options over the fundamental returns-only estimation on GARCH models. From our empirical studies, with the additional option sample, we can improve the efficiency of the estimates for HN-GARCH parameters. Nonetheless, the improvements for the risk premium factor, both from empirical standard errors, and sample RMSEs, are insignificant. In addition, option prices are simulated with a pre-defined noise structure and …

A Class Of Phase-Type Ageing Models And Their Lifetime Distributions, Boquan Cheng

Electronic Thesis and Dissertation Repository

Ageing is a universal and ever-present biological phenomenon. Yet, describing the ageing mechanism in formal mathematical terms — in particular, capturing the ageing pattern and quantifying the ageing rate — has remained a challenging actuarial modelling endeavour. In this thesis, we propose a class of Coxian-type Markovian models. This class enables a quantitative description of the well-known characteristics of ageing, which is a genetically determined, progressive, and essentially irreversible process. The unique structure of our model features the transition rate for the ageing process and a functional form for the relationship between ageing and death with a shape parameter that …

The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications, Zhenxian Gong

Electronic Thesis and Dissertation Repository

Financial markets and instruments are continuously evolving, displaying new and more refined stylized facts. This requires regular reviews and empirical evaluations of advanced models. There is evidence in literature that supports stochastic volatility models over constant volatility models in capturing stylized facts such as "smile" and "skew" presented in implied volatility surfaces. In this thesis, we target commodity and volatility index markets, and develop a novel stochastic volatility model that incorporates mean-reverting property and 4/2 stochastic volatility process. Commodities and volatility indexes have been proved to be mean-reverting, which means their prices tend to revert to their long term mean …

Statistical Methods With A Focus On Joint Outcome Modeling And On Methods For Fire Science, Da Zhong Xi

Electronic Thesis and Dissertation Repository

Understanding the dynamics of wildfires contributes significantly to the development of fire science. Challenges in the analysis of historical fire data include defining fire dynamics within existing statistical frameworks, modeling the duration and size of fires as joint outcomes, identifying the how fires are grouped into clusters of subpopulations, and assessing the effect of environmental variables in different modeling frameworks. We develop novel statistical methods to consider outcomes related to fire science jointly. These methods address these challenges by linking univariate models for separate outcomes through shared random effects, an approach referred to as joint modeling. Comparisons with existing …

Renewable-Energy Resources, Economic Growth And Their Causal Link, Yiyang Chen

Electronic Thesis and Dissertation Repository

This thesis examines the presence and strength of predictive causal relationship between re-newable energy prices and economic growth. We look for evidence by investigating the cases of Norway, New Zealand, and Canada’s two provinces of Alberta and Ontario. The usual vectorautoregressive model (VAR) and its various improved versions still assume constant parametersover time. We devise a Markov-switching VAR (MS-VAR) model in order to accommodate the observed time-dependent causal relation changes. Our proposed modelling approach is induced by the hidden Markov model methodologies in terms of an online parameter estimationthrough recursive filtering. The parameters of the MS-VAR model are governed by …

Extensions Of Classification Method Based On Quantiles, Yuanhao Lai

Electronic Thesis and Dissertation Repository

This thesis deals with the problem of classification in general, with a particular focus on heavy-tailed or skewed data. The classification problem is first formalized by statistical learning theory and several important classification methods are reviewed, where the distance-based classifiers, including the median-based classifier and the quantile-based classifier (QC), are especially useful for the heavy-tailed or skewed inputs. However, QC is limited by its model capacity and the issue of high-dimensional accumulated errors. Our objective of this study is to investigate more general methods while retaining the merits of QC.

We present four extensions of QC, which appear in chronological …

Generalized 4/2 Factor Model, Yuyang Cheng

Electronic Thesis and Dissertation Repository

We investigate portfolio optimization, risk management, and derivative pricing for a factor stochastic model that considers the 4/2 stochastic volatility on the common/systematic factor as well as on the intrinsic factor. This setting allows us to capture stochastic volatility and stochastic covariation among assets. The model is also a generalization of existing models in the literature as it includes the mean reverting property and spillover effect to capture wider types of financial assets. At a theoretical level we identify conditions for well-defined changes of measure. A quasi-closed form solution within a 4/2 structured model is obtained for a portfolio optimization …

Edge-Cloud Iot Data Analytics: Intelligence At The Edge With Deep Learning, Ananda Mohon M. Ghosh

Electronic Thesis and Dissertation Repository

Rapid growth in numbers of connected devices, including sensors, mobile, wearable, and other Internet of Things (IoT) devices, is creating an explosion of data that are moving across the network. To carry out machine learning (ML), IoT data are typically transferred to the cloud or another centralized system for storage and processing; however, this causes latencies and increases network traffic. Edge computing has the potential to remedy those issues by moving computation closer to the network edge and data sources. On the other hand, edge computing is limited in terms of computational power and thus is not well suited for …

Point Process Modelling Of Objects In The Star Formation Complexes Of The M33 Galaxy, Dayi Li

Electronic Thesis and Dissertation Repository

In this thesis, Gibbs point process (GPP) models are constructed to study the spatial distribution of objects in the star formation complexes of the M33 galaxy. The GPP models circumvent the limitations of the two-point correlation function employed in the current astronomy literature by naturally accounting for the inhomogeneous distribution of these objects. The spatial distribution of these objects serves as a sensitive probe in understanding the star formation process, which is crucial in understanding the formation of galaxies and the Universe. The objects under study include the CO filament structure, giant molecular clouds (GMCs) and young stellar cluster candidates …

Statistical Modeling And Characterization Of Induced Seismicity Within The Western Canada Sedimentary Basin, Sid Kothari

Electronic Thesis and Dissertation Repository

In western Canada, there has been an increase in seismic activity linked to anthropogenic energy-related operations including conventional hydrocarbon production, wastewater fluid injection and more recently hydraulic fracturing (HF). Statistical modeling and characterization of the space, time and magnitude distributions of the seismicity clusters is vital for a better understanding of induced earthquake processes and development of predictive models. In this work, a statistical analysis of the seismicity in the Western Canada Sedimentary Basin was performed across past and present time periods by utilizing a compiled earthquake catalogue for Alberta and eastern British Columbia. Specifically, the frequency-magnitude statistics were analyzed …

Exploring The Estimability Of Mark-Recapture Models With Individual, Time-Varying Covariates Using The Scaled Logit Link Function, Jiaqi Mu

Electronic Thesis and Dissertation Repository

Mark-recapture studies are often used to estimate the survival of individuals in a population and identify factors that affect survival in order to understand how the population might be affected by changing conditions. Factors that vary between individuals and over time, like body mass, present a challenge because they can only be observed when an individual is captured. Several models have been proposed to deal with the missing-covariate problem and commonly impose a logit link function which implies that the survival probability varies between 0 and 1. In this thesis I explore the estimability of four possible models when survival …

Split Credibility: A Two-Dimensional Semi-Linear Credibility Model, Jingbing Qiu

Electronic Thesis and Dissertation Repository

In the thesis, we introduce a two-dimensional semi-linear credibility model, which is an extension of the classical credibility or split credibility models used by practicing actuaries. Our model predicts the future expected losses of a policyholder by considering its historical primary and excess losses. The optimal split point is derived based on the mean squared error criterion. We show when and why splitting a policyholder’s historical losses into primary and excess parts work analytically. In addition, we derived formulas for estimating our model parameters nonparametrically. Finally, we show the application of our model through three examples.

Bias Assessment And Reduction In Kernel Smoothing, Wenkai Ma

Electronic Thesis and Dissertation Repository

When performing local polynomial regression (LPR) with kernel smoothing, the choice of the smoothing parameter, or bandwidth, is critical. The performance of the method is often evaluated using the Mean Square Error (MSE). Bias and variance are two components of MSE. Kernel methods are known to exhibit varying degrees of bias. Boundary effects and data sparsity issues are two potential problems to watch for. There is a need for a tool to visually assess the potential bias when applying kernel smooths to a given scatterplot of data. In this dissertation, we propose pointwise confidence intervals for bias and demonstrate a …

Statistical Applications In Healthcare Systems, Maryam Mojalal

Electronic Thesis and Dissertation Repository

This thesis consists of three contributing manuscripts related to waiting times with possible applications in health care. The first manuscript is inspired by a practical problem related to decision making in an emergency department (ED). As short-run predictions of ED censuses are particularly important for efficient allocation and management of ED resources we model ED changes and present estimations for short term (hourly) ED censuses at each time point. We present a Markov-chain based algorithm to make census predictions in near future.

Considering the variation in arrival pattern and service requirements, we apply and compare three models which best describe …

Modelling The Common Risk Among Equities Using A New Time Series Model, Jingjia Chu

Electronic Thesis and Dissertation Repository

A new additive structure of multivariate GARCH model is proposed where the dynamic changes of the conditional correlation between the stocks are aggregated by the common risk term. The observable sequence is divided into two parts, a common risk term and an individual risk term, both following a GARCH type structure. The conditional volatility of each stock will be the sum of these two conditional variance terms. All the conditional volatility of the stock can shoot up together because a sudden peak of the common volatility is a sign of the system shock.

We provide sufficient conditions for strict stationarity …

Some Applications Of Higher-Order Hidden Markov Models In The Exotic Commodity Markets, Heng Xiong

Electronic Thesis and Dissertation Repository

The liberalisation of regional and global commodity markets over the last several decades resulted in certain commodity price behaviours that require new modelling and estimation approaches. Such new approaches have important implications to the valuation and utilisation of commodity derivatives. Derivatives are becoming increasingly crucial for market participants in hedging their exposure to volatile price swings and in managing risks associated with derivative trading. The modelling of commodity-based variables is an integral part of risk management and optimal-investment strategies for commodity-linked portfolios. The characteristics of commodity price evolution cannot be captured sufficiently by one-state driven models even with the inclusion …

Statistical Modelling, Optimal Strategies And Decisions In Two-Period Economies, Jiang Wu

Electronic Thesis and Dissertation Repository

Motivated by some real problems, our thesis puts forward two general two-period pricing models and explore optimal buying and selling strategies in two states of the two-period decision, when buyer/seller's decisions in the two periods are uncertain: commodity valuations may or may not be independent, may or may not follow the same distribution, be heavily or just lightly influenced by exogenous economic conditions, and so on. For both the example of buying laptops and the example of selling houses, the connections between each example and the two-envelope paradox encourage us to explore optimal strategies based on the works of McDonnell …

Data-Adaptive Kernel Support Vector Machine, Xin Liu

Electronic Thesis and Dissertation Repository

In this thesis, we propose the data-adaptive kernel Support Vector Machine (SVM), a new method with a data-driven scaling kernel function based on real data sets. This two-stage approach of kernel function scaling can enhance the accuracy of a support vector machine, especially when the data are imbalanced. Followed by the standard SVM procedure in the first stage, the proposed method locally adapts the kernel function to data locations based on the skewness of the class outcomes. In the second stage, the decision rule is constructed with the data-adaptive kernel function and is used as the classifier. This process enlarges …

On The Estimation Of Penetrance In The Presence Of Competing Risks With Family Data, Daniel Prawira

Electronic Thesis and Dissertation Repository

In family studies, we are interested in estimating the penetrance function of the event of interest in the presence of competing risks. Failure to account for competing risks may lead to bias in the estimation of the penetrance function. In this thesis, three statistical challenges are addressed: clustering, missing data, and competing risks. We proposed the cause-specific model with shared frailty and ascertainment correction to account for clustering and competing risks along with ascertainment of families into study. Multiple imputation is used to account for missing data. The simulation study showed good performance of our proposed model in estimating the …

Annuity Product Valuation And Risk Measurement Under Correlated Financial And Longevity Risks, Soohong Park

Electronic Thesis and Dissertation Repository

Longevity risk is a non-diversifiable risk and regarded as a pressing socio-economic challenge of the century. Its accurate assessment and quantification is therefore critical to enable pension-fund companies provide sustainable old-age security and maintain a resilient global insurance market. Fluctuations and a decreasing trend in mortality rates, which give rise to longevity risk, as well as the uncertainty in interest-rate dynamics constitute the two fundamental determinants in pricing and risk management of longevity-dependent products. We also note that historical data reveal some evidence of strong correlation between mortality and interest rates and must be taken into account when modelling their …

Classification With Large Sparse Datasets: Convergence Analysis And Scalable Algorithms, Xiang Li

Electronic Thesis and Dissertation Repository

Large and sparse datasets, such as user ratings over a large collection of items, are common in the big data era. Many applications need to classify the users or items based on the high-dimensional and sparse data vectors, e.g., to predict the profitability of a product or the age group of a user, etc. Linear classifiers are popular choices for classifying such datasets because of their efficiency. In order to classify the large sparse data more effectively, the following important questions need to be answered.

1. Sparse data and convergence behavior. How different properties of a dataset, such as …