Physical Sciences and Mathematics Commons^™

Anisotropic Kernel Smoothing For Change-Point Data With An Analysis Of Fire Spread Rate Variability, John Ronald James Thompson

Electronic Thesis and Dissertation Repository

Wildland fires are natural disturbances that enable the renewal of forests. However, these fires also place public safety and property at risk. Understanding forest fire spread in any region of Canada is critical to promoting forest health, and protecting human life and infrastructure. In 2014, Ontario updated its Wildland Fire Management Strategy, moving away from ``zone-based" decision making to ``appropriate response" decision making. This new strategy calls for an assessment of the risks and benefits of every wildland fire reported in the province. My research places the emphasis on the knowledge and understanding of fire spread rates and their variabilities. …

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 …

Analysis Challenges For High Dimensional Data, Bangxin Zhao

Electronic Thesis and Dissertation Repository

In this thesis, we propose new methodologies targeting the areas of high-dimensional variable screening, influence measure and post-selection inference. We propose a new estimator for the correlation between the response and high-dimensional predictor variables, and based on the estimator we develop a new screening technique termed Dynamic Tilted Current Correlation Screening (DTCCS) for high dimensional variables screening. DTCCS is capable of picking up the relevant predictor variables within a finite number of steps. The DTCCS method takes the popular used sure independent screening (SIS) method and the high-dimensional ordinary least squares projection (HOLP) approach as its special cases.

Two methods …

Computational Modelling Of Human Transcriptional Regulation By An Information Theory-Based Approach, Ruipeng Lu

Electronic Thesis and Dissertation Repository

ChIP-seq experiments can identify the genome-wide binding site motifs of a transcription factor (TF) and determine its sequence specificity. Multiple algorithms were developed to derive TF binding site (TFBS) motifs from ChIP-seq data, including the entropy minimization-based Bipad that can derive both contiguous and bipartite motifs. Prior studies applying these algorithms to ChIP-seq data only analyzed a small number of top peaks with the highest signal strengths, biasing their resultant position weight matrices (PWMs) towards consensus-like, strong binding sites; nor did they derive bipartite motifs, disabling the accurate modelling of binding behavior of dimeric TFs.

This thesis presents a novel …

Advances In Semi-Nonparametric Density Estimation And Shrinkage Regression, Hossein Zareamoghaddam

Electronic Thesis and Dissertation Repository

This thesis advocates the use of shrinkage and penalty techniques for estimating the parameters of a regression model that comprises both parametric and nonparametric components and develops semi-nonparametric density estimation methodologies that are applicable in a regression context.

First, a moment-based approach whereby a univariate or bivariate density function is approximated by means of a suitable initial density function that is adjusted by a linear combination of orthogonal polynomials is introduced. Such adjustments are shown to be mathematically equivalent to making use of standard polynomials in one or two variables. Once extended to apply to density estimation, in which case …

Advances In The Modeling Of Heavy-Tailed Distributions, Sang Jin Kang

Electronic Thesis and Dissertation Repository

Several advances are proposed in connection with the approximation and estimation of heavy-tailed distributions, some of which also apply to other types of distributions. It is first explained that on initially applying the Esscher transform to heavy-tailed density functions such as the Pareto, Student-t and Cauchy densities, one can utilize a moment-based technique whereby the tilted density functions are expressed as the product of a base density function and a polynomial adjustment. Alternatively, density approximants can be secured by appropriately truncating the distributions or mapping them onto compact supports. The validity of these approaches is corroborated by simulation studies. …