An exploration of self-deception in proslavery arguments in the antebellum South. This work explores how proslavery theorists were able to support slavery despite overwhelming evidence that slavery was immoral. By using non-intentional self-deception, slavery supporters tested their hypothesis that slavery was good in a motivationally biased manner that aligned with their interests and desires.

Incompleteness is a major feature of time-to-event data. As one type of incompleteness, truncation refers to the unobservability of the time-to-event variable because it is smaller (or greater) than the truncation variable. A truncated sample always involves left and right truncation. Left truncation has been studied extensively while right truncation has not received the same level of attention. In one of the earliest studies on right truncation, Lagakos et al. (1988) proposed to transform a right truncated variable to a left truncated variable and then apply existing methods to the transformed variable. The reverse-time hazard function is introduced through transformation. However, this quantity does not have a natural interpretation. There exist gaps in the inferences for the regular forward-time hazard function with right truncated data. This dissertation discusses variance estimation of the cumulative hazard estimator, one-sample log-rank test, and comparison of hazard rate functions among finite independent samples under the context of right truncation. First, the relation between the reverse- and forward-time cumulative hazard functions is clarified. This relation leads to the nonparametric inference for the cumulative hazard function. Jiang (2010) recently conducted a research on this direction and proposed two variance estimators of the cumulative hazard estimator. Some revision to the variance estimators is suggested in this dissertation and evaluated in a Monte-Carlo study. Second, this dissertation studies the hypothesis testing for right truncated data. A series of tests is developed with the hazard rate function as the target quantity. A one-sample log-rank test is first discussed, followed by a family of weighted tests for comparison between finite $K$-samples. Particular weight functions lead to log-rank, Gehan, Tarone-Ware tests and these three tests are evaluated in a Monte-Carlo study. Finally, this dissertation studies the nonparametric inference for the hazard rate function for the right truncated data. The kernel smoothing technique is utilized in estimating the hazard rate function. A Monte-Carlo study investigates the uniform kernel smoothed estimator and its variance estimator. The uniform, Epanechnikov and biweight kernel estimators are implemented in the example of blood transfusion infected AIDS data.

This thesis consists of four papers dealing with estimation and inference for quantile regression of longitudinal data, with an emphasis on nonlinear models. The first paper extends the idea of quantile regression estimation from the case of cross-sectional data with independent errors to the case of linear or nonlinear longitudinal data with dependent errors, using a weighted estimator. The performance of different weights is evaluated, and a comparison is also made with the corresponding mean regression estimator using the same weights. The second paper examines the use of bootstrapping for bias correction and calculations of confidence intervals for parameters of the quantile regression estimator when longitudinal data are used. Different weights, bootstrap methods, and confidence interval methods are used. The third paper is devoted to evaluating bootstrap methods for constructing hypothesis tests for parameters of the quantile regression estimator using longitudinal data. The focus is on testing the equality between two groups of one or all of the parameters in a regression model for some quantile using single or joint restrictions. The tests are evaluated regarding both their significance level and their power. The fourth paper analyzes seven longitudinal data sets from different parts of the biostatistics area by quantile regression methods in order to demonstrate how new insights can emerge on the properties of longitudinal data from using quantile regression methods. The quantile regression estimates are also compared and contrasted with the least squares mean regression estimates for the same data set. In addition to looking at the estimates, confidence intervals and hypothesis testing procedures are examined.

An important problem in statistical inference is to check the adequacy of models upon which inferences are based. Some valuable tools are available for examining a model's suitability of which the most widely used is the goodness-of-fit test. The pioneering work in this area is by Karl Pearson (1900). Since then, a considerable amount of work has been done so far and investigation is still going on in this field due to its importance in the hypothesis testing problem.This thesis contains an expository discussion of the goodness-of-fit tests, intended for the users of the statistical theory. An attempt is made here to give a complete coverage of the historical development, present status and other current problems related to this topic. Numerical examples are provided to best explain the test procedures. The contents, taken as a whole, constitute a unified presentation of some of the most important aspects of goodness-of-fit tests.Ball State UniversityMuncie, IN 57406

The Empirical Likelihood method (ELM) was introduced by A. B. Owen to test hypotheses in the early 1990s. It's a nonparametric method and uses the data directly to do statistical tests and to compute confidence intervals/regions. Because of its distribution free property and generality, it has been studied extensively and employed widely in statistical topics. There are many classical test statistics such as the Cramer-von Mises (CM) test statistic, the Anderson-Darling test statistic, and the Watson test statistic, to name a few. However, none is universally most powerful. This thesis is dedicated to extending the ELM to several interesting statistical topics in hypothesis tests. First of all, we focus on testing the fit of distributions. Based on the CM test, we propose a novel Jackknife Empirical Likelihood test via estimating equations in testing the goodness-of-fit. The proposed new test allows one to add more relevant constraints so as to improve the power. Also, this idea can be generalized to other classical test statistics. Second, when aiming at testing the error distributions generated from a statistical model (e.g., the regression model), we introduce the Jackknife Empirical Likelihood idea to the regression model, and further compute the confidence regions with the merits of distribution free limiting chi-square property. Third, the ELM based on some weighted score equations are proposed for constructing confidence intervals for the coefficient in the simple bilinear model. The effectiveness of all presented methods are demonstrated by some extensive simulation studies.

Cluster analysis is one of the typical tasks in Data Mining, and it groups data objects based only on information found in the data that describes the objects and their relationships. The purpose of this thesis is to verify a modified K-means algorithm in asymmetrical cases, which can be regarded as an extension to the research of Vladislav Valkovsky and Mikael Karlsson in Department of Informatics and Media. In this thesis an experiment is designed and implemented to identify clusters with the modified algorithm in asymmetrical cases. In the experiment the developed Java application is based on knowledge established from previous research. The development procedures are also described and input parameters are mentioned along with the analysis. This experiment consists of several test suites, each of which simulates the situation existing in real world, and test results are displayed graphically. The findings mainly emphasize the limitations of the algorithm, and future work for digging more essences of the algorithm is also suggested.

We are concerned with testing for differential expression and consider three different aspects of such testing procedures. First, we develop an exact ANOVA type model for discrete gene expression data, produced by technologies such as a Massively Parallel Signature Sequencing (MPSS), Serial Analysis of Gene Expression (SAGE) or other next generation sequencing technologies. We adopt two Bayesian hierarchical models—one parametric and the other semiparametric with a Dirichlet process prior that has the ability to borrow strength across related signatures, where a signature is a specific arrangement of the nucleotides. We utilize the discreteness of the Dirichlet process prior to cluster signatures that exhibit similar differential expression profiles. Tests for differential expression are carried out using non-parametric approaches, while controlling the false discovery rate. Next, we consider ways to combine expression data from different studies, possibly produced by different technologies resulting in mixed type responses, such as Microarrays and MPSS. Depending on the technology, the expression data can be continuous or discrete and can have different technology dependent noise characteristics. Adding to the difficulty, genes can have an arbitrary correlation structure both within and across studies. Performing several hypothesis tests for differential expression could also lead to false discoveries. We propose to address all the above challenges using a Hierarchical Dirichlet process with a spike-and-slab base prior on the random effects, while smoothing splines model the unknown link functions that map different technology dependent manifestations to latent processes upon which inference is based. Finally, we propose an algorithm for controlling different error measures in a Bayesian multiple testing under generic loss functions, including the widely used uniform loss function. We do not make any specific assumptions about the underlying probability model but require that indicator variables for the individual hypotheses are available as a component of the inference. Given this information, we recast multiple hypothesis testing as a combinatorial optimization problem and in particular, the 0-1 knapsack problem which can be solved efficiently using a variety of algorithms, both approximate and exact in nature.

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Energy or DFT detector using a fixed window size is very efficient when signal start time and duration is matched with that of the window&#039 / s. However, in the case of unknown signal duration, the performance of this detector decreases. For this scenario, a detector system composed of multiple windows may be preferred. Window sizes of such a system will also be fixed beforehand but they will be different from each other. Therefore, one of the windows will better match the signal duration, giving better detection results. In this study, multiple window detectors are analyzed. Their false alarm and detection probability relations are investigated. Some exact and approximate values are derived for these probabilities. A rule of thumb for the choice of window lengths is suggested for the case of fixed number of windows. Detectors with overlapping window structure are considered for the signals with unknown delay. Simulation results are added for these types of detectors.

Knowledge of fire risk is crucial for manufacturers and regulators to make correct choices in prescribing fire protection systems, especially flame retardants. Methods of determining fire risk are bogged down by a multitude of confounding factors, such as population demographics and overlapping fire protection systems. Teasing out the impacts of one particular choice or regulatory change in such an environment is crucial. Teasing out such detail requires statistical techniques, and knowledge of the field is important for verifying potential methods. Comparing the fire problems between two states might be one way to identify successful approaches to fire safety. California, a state with progressive fire prevention policies, is compared to Texas using logistic regression modeling to account for various common factors such as percentage of rural population and percentage of population in ‘risky’ age brackets. Results indicate that living room fires, fires in which the first item ignited is a flammable liquid, piping, or filter, and fires started by cigarettes, pipes, and cigars have significantly higher odds of resulting in a casualty or fatality than fires started by other areas of origin, items first ignited, or heat sources. Additionally, fires in Texas have roughly 1.5 times higher odds of resulting in casualties than fires in California for certain areas of origin, items first ignited, and heat sources. Methods of estimating fire losses are also examined. The potential of using Ramachandran’s power-law relationship to estimate fire losses in residential home fires in Texas is examined, and determined to be viable but not discriminating. CFAST is likewise explored as a means to model fire losses. Initial results are inconclusive, but Monte Carlo simulation of home geometries might render the approach viable. / text