Physical Sciences and Mathematics Commons^™

Estimating The Coefficients Of A Linear Differential Operator, Maria Ivette Barraza

Open Access Theses & Dissertations

Principal Differential Analysis (PDA; Ramsay, 1996) is used to obtain low dimensional representations of functional data, where each observation is represented as a curve. PDA seeks to identify a Linear Differential Operator (LDO) L = ω0I + ω 1D + ... + ωmDm, where I denotes the identity function and D j the jth derivative, that satisfies as closely as possible that Lx = 0 for each functional observation x. A theorem from analysis establishes that the coefficients of the LDO are in the Sobolev space, and thus can be approximated by B-splines. Current PDA software used to estimate the …

Predicting Individualized Treatment Effects Via Random Forests Of Interaction Trees, Annette Pena Franco

Open Access Theses & Dissertations

Abstract Not Available

Analysis Of Bias-Corrected And Exact Estimators For Binomial Generalized Linear Model Parameters, Hamna Hannan

Open Access Theses & Dissertations

Typically, small samples have always been a problem for binomial generalized linear models. Though generalized linear models are widely popular in public health, social sciences etc. In small sample scenarios the non-existence of the maximum likelihood (ML) estimators is very common as well as separation occurs in the data. In logistic regression the maximum likelihood estimates are found to have biased away from origin. My work examines the bias-reduced and exact estimators that have been used to estimate the slope parameters and standard errors of the estimated slope parameters as compared to the traditional ML method.

The present work is …

The Nonparametric Estimation Of Elliptical Distributions, Panfeng Liang

Open Access Theses & Dissertations

In practice, many multivariate datasets have identical marginal distributions. Elliptical distributions can be used to model many of those datasets. In this Thesis, we will propose a Bayesian method using Markov chain Monte Carlo (MCMC) methods to estimate the density function underlying multivariate datasets assuming it is an elliptical distribution.

Sample Size Estimation For Linear Mixed Models With Dependent End Points, Michael Nsiah-Nimo

Open Access Theses & Dissertations

The primary objective is sample size estimation in linear mixed model settings. Sample size estimation is an important component of planning a well thought out scientific experiment. Whenever sample size estimation is performed, taking into account a priori model based inferences will provide a sample size estimate that will achieve the desired power without inflating the type I error rate of the study.

One common practice is a traditional approach cited in the literature that uses the largest sample size after you Bonferroni the type I error rate to estimate sample sizes as such. We are going to take into …

Evaluating Binary Splits On Nominal Inputs, Isaac Xoese Ocloo

Open Access Theses & Dissertations

The maximally selected statistic approach in building tree models is shown to be a cause of variable selection bias. In this study we propose three methods to solve this problem in building regression trees with nominal predictor variables. Out of the three methods

proposed we explored only two in detail and defer one for further research. We developed an exact method to compute the p-value corresponding to the maximized splitting statistic in regression trees for nominal predictor variables with at most 10 distinct levels and a

method to estimate the best cutoff point as a parameter in a parametric nonlinear …