Physical Sciences and Mathematics Commons^™

Censored Time Series Analysis, Nagham Muslim Mohammad

Electronic Thesis and Dissertation Repository

Environmental data is frequently left or right censored. This is due to the fact that the correct value for observed values that are below or above some threshold or detection point are inaccurate so that it is only known for sure that the true value is below or above that threshold. This is frequently important with water quality and air quality time series data. Interval censoring occurs when the correct values of the data are known only for those values falling above some lower threshold and below some upper threshold. Censoring threshold values may change over time, so multiple censor …

Perfect And Nearly Perfect Sampling Of Work-Conserving Queues, Yaofei Xiong

Electronic Thesis and Dissertation Repository

We present sampling-based methods to treat work-conserving queueing systems. A variety of models are studied. Besides the First Come First Served (FCFS) queues, many efforts are putted on the accumulating priority queue (APQ), where a customer accumulates priority linearly while waiting. APQs have Poisson arrivals, multi-class customers with corresponding service durations, and single or multiple servers.

Perfect sampling is an approach to draw a sample directly from the steady-state distribution of a Markov chain without explicitly solving for it. Statistical inference can be conducted without initialization bias. If an error can be tolerated within some limit, i.e. the total variation …

The Doubly Adaptive Lasso Methods For Time Series Analysis, Zi Zhen Liu

Electronic Thesis and Dissertation Repository

In this thesis, we propose a systematic approach called the doubly adaptive LASSO tailored to time series analysis, which includes four specific methods for four time series models, respectively:

The PAC-weighted adaptive LASSO for univariate autoregressive (AR) models. Although the LASSO methodology has been applied to AR models, the existing methods in the literature ignore the temporal dependence information embedded in AR time series data. Consequently, the methods may not reflect the characteristics of underlying AR processes, especially, the lag order of AR models. The PAC-weighted adaptive LASSO incorporates the partial autocorrelation (PAC) into the adaptive LASSO weights. The PAC-weighted …

Risk Models With Dependence And Perturbation, Zhong Li

Electronic Thesis and Dissertation Repository

In ruin theory, the surplus process of an insurance company is usually modeled by the classical compound Poisson risk model or its general version, the Sparre-Andersen risk model. Under these models, the claim amounts and the inter-claim times are assumed to be independently distributed, which is not always appropriate in practice. In recent years, risk models relaxing the independence assumption have drawn increasing attention. However, previous research mostly considers the so call dependent Sparre-Andersen risk model under which the pairs of random variables consisting of the inter-claim time and the next claim amount remain independent of each other. In this …

Identification Of Informativeness In Text Using Natural Language Stylometry, Rushdi Shams

Electronic Thesis and Dissertation Repository

In this age of information overload, one experiences a rapidly growing over-abundance of written text. To assist with handling this bounty, this plethora of texts is now widely used to develop and optimize statistical natural language processing (NLP) systems. Surprisingly, the use of more fragments of text to train these statistical NLP systems may not necessarily lead to improved performance. We hypothesize that those fragments that help the most with training are those that contain the desired information. Therefore, determining informativeness in text has become a central issue in our view of NLP. Recent developments in this field have spawned …

Valuation And Risk Measurement Of Guaranteed Annuity Options Under Stochastic Environment, Huan Gao

Electronic Thesis and Dissertation Repository

This thesis develops stochastic modelling frameworks for the accurate pricing and risk management of complex insurance products with option-embedded features. We propose stochastic models for the evolution of the two main risk factors, the interest rate and mortality rate, which could also have a correlation structure. For the valuation problem, a general framework is put forward where correlated interest and mortality rates are modelled as affine-diffusion processes. A new concept of endowment-risk-adjusted measure is introduced to facilitate the calculation of the GAO value. As a natural offshoot of addressing GAO valuation, we derive the convex-order upper and lower bounds of …

Estimation Of Hidden Markov Models And Their Applications In Finance, Anton Tenyakov

Electronic Thesis and Dissertation Repository

Movements of financial variables exhibit extreme fluctuations during periods of economic crisis and times of market uncertainty. They are also affected by institutional policies and intervention of regulatory authorities. These structural changes driving prices and other economic indicators can be captured reasonably by models featuring regime-switching capabilities. Hidden Markov models (HMM) modulating the model parameters to incorporate such regime-switching dynamics have been put forward in recent years, but many of them could still be further improved. In this research, we aim to address some of the inadequacies of previous regime-switching models in terms of their capacity to provide better forecasts …

A Spatial Analysis Of Forest Fire Survival And A Marked Cluster Process For Simulating Fire Load, Amy A. Morin

Electronic Thesis and Dissertation Repository

The duration of a forest fire depends on many factors, such as weather, fuel type and fuel moisture, as well as fire management strategies. Understanding how these impact the duration of a fire can lead to more effective suppression efforts as this information can be incorporated into decision support systems used by fire management agencies to help allocate suppression resources. This thesis presents a thorough survival analysis of lightning and people-caused fires in the Intensive fire management zone of Ontario, Canada from 1989 through 2004. The analysis is then extended to investigate spatial patterns across this region using proportional hazards …

Statistical Applications In Wildfire Management And Prediction, Lengyi Han

Electronic Thesis and Dissertation Repository

This thesis develops statistical methods and models and applies them
to problems related to forest fires. The unifying goal of the work is to provide a data analytic basis for quantifying the uncertainty surrounding fire ignition and fire growth which builds on existing theory where possible.

The main body of the thesis is comprised of three research papers. The Fire Weather Index (FWI) plays an important role in fire management and is central to the first two papers. In the first instance, the block bootstrap confidence interval method is used to deal nonparametrically with the dependence in the FWI data. …

Decision Theory Based Models In Insurance And Beyond, Raymond Ye Zhang

Electronic Thesis and Dissertation Repository

Everyday, we make difficult choices under uncertainties. The decision making process becomes even more complicated when more agents get involved: one must consider their interactions and conflicts of interest because the final outcome is based not only on an agent's decision but on everybody's.

In insurance industry, companies try to avoid making large claim payments to policyholders (commonly known as insureds) by purchasing reinsurance policies from reinsurance companies (the reinsurer). Each policy details conditions upon which the reinsurer pays a share of the claim to the insurance company (also known as the cedent or the insurer). To reach an agreement, …

Statistical Methods For The Analysis Of Rna Sequencing Data, Man-Kee Maggie Chu

Electronic Thesis and Dissertation Repository

The next generation sequencing technology, RNA-sequencing (RNA-seq), has an increasing popularity over traditional microarrays in transcriptome analyses. Statistical methods used for gene expression analyses with these two technologies are different because the array-based technology measures intensities using continuous distributions, whereas RNA-seq provides absolute quantification of gene expression using counts of reads. There is a need for reliable statistical methods to exploit the information from the rapidly evolving sequencing technologies and limited work has been done on expression analysis of time-course RNA-seq data. In this dissertation, we propose a model-based clustering method for identifying gene expression patterns in time-course RNA-seq data. …

Computing And Approximation Methods For The Distribution Of Multivariate Aggregate Claims, Tao Jin

Electronic Thesis and Dissertation Repository

Insurance companies typically face multiple sources (types) of claims. Therefore, modeling dependencies among different types of risks is extremely important for evaluating the aggregate claims of an insurer. In the first part of this thesis, we consider three classes of bivariate counting distributions and the corresponding compound distributions introduced in a 1996 paper by Hesselager. We implement the recursive methods for computing the joint probability functions derived by Hesselager and then compare the results with those obtained from fast Fourier transform (FFT) methods. In applying the FFT methods, we extend the concept of exponential tilting for univariate FFT proposed by …