Generalized Anxiety Disorder (GAD) is one of the most common and impairing childhood anxiety disorders, impacting over 10% of children with an average age of onset at 8.5 years. GAD in childhood increases the risk for developing additional anxiety and depressive disorders, academic and social difficulties, and, if left untreated, continuity into adulthood. While treatments incorporating mindfulness techniques have been shown to be efficacious among adults, relatively few studies have examined the efficacy of these techniques in the treatment of children. Mindfulness skills may be able to target maladaptive cognitive patterns by teaching children more flexible ways of thinking and viewing the world and providing children additional coping skills that may positively impact their overall functioning long-term. The aim of the present study was to develop and provide preliminary evaluation of a mindfulness-based intervention for GAD in school-aged children. Four children aged 9 to 12 with a principal diagnosis of GAD completed an open trial pilot phase of a 6-session individual format mindfulness intervention. Each session emphasized mindful awareness of breath, body, and thoughts, and involved child and parent participation. An additional twelve children were randomized to either an immediate treatment (n = 6) or a waitlist (i.e., delayed treatment; n = 6) condition during the course of a randomized waitlist-controlled clinical trial. Measures were administered at pre-waitlist (if applicable), post-waitlist/pre-treatment, post-treatment, and eight weeks following treatment to assess overall program satisfaction and changes in symptoms and diagnosis. Overall, treatment dropout was low, and families reported high satisfaction with treatment. Relative to waitlist, children in the immediate treatment group evidenced significant difference in mean change scores on Clinical Global Improvement Severity score and Child Behavioral Checklist Internalizing and Anxiety Problems scales. Effect size statistics indicated very large effect sizes between the waitlist and immediate treatment groups for change in GAD Clinical Severity Rating, child self-report of worries, and mindfulness ability, despite non-statistical significance. Overall, the intervention demonstrated feasibility, acceptability, and preliminary evidence of potential efficacy even in this small pilot study. Effect size estimates suggest a larger randomized clinical trial is warranted to fully evaluate treatment efficacy.

abstract: Schennach (2007) has shown that the Empirical Likelihood (EL) estimator may not be asymptotically normal when a misspecified model is estimated. This problem occurs because the empirical probabilities of individual observations are restricted to be positive. I find that even the EL estimator computed without the restriction can fail to be asymptotically normal for misspecified models if the sample moments weighted by unrestricted empirical probabilities do not have finite population moments. As a remedy for this problem, I propose a group of alternative estimators which I refer to as modified EL (MEL) estimators. For correctly specified models, these estimators have the same higher order asymptotic properties as the EL estimator. The MEL estimators are obtained by the Generalized Method of Moments (GMM) applied to an exactly identified model. The simulation results provide promising evidence for these estimators. In the second chapter, I introduce an alternative group of estimators to the Generalized Empirical Likelihood (GEL) family. The new group is constructed by employing demeaned moment functions in the objective function while using the original moment functions in the constraints. This designation modifies the higher-order properties of estimators. I refer to these new estimators as Demeaned Generalized Empirical Likelihood (DGEL) estimators. Although Newey and Smith (2004) show that the EL estimator in the GEL family has fewer sources of bias and is higher-order efficient after bias-correction, the demeaned exponential tilting (DET) estimator in the DGEL group has those superior properties. In addition, if data are symmetrically distributed, every estimator in the DGEL family shares the same higher-order properties as the best member.   / Dissertation/Thesis / Ph.D. Economics 2013

M.Sc.

Introduction: Alzheimer’s disease is an irreversible brain disorder characterized by distortion of memory and other mental functions. Although, several psychometric tests are available for diagnosis of Alzheimer’s, there is a great concern about the validity of these tests at recognizing the early onset of the disease. Currently, brain magnetic resonance imaging is not commonly utilized in the diagnosis of Alzheimer’s, because researchers are still puzzled by the association of brain regions with the disease status and its progress. Moreover, MRI data tend to be of high dimensional nature requiring advanced statistical methods to accurately analyze them. In the past decade, the application of Least Absolute Shrinkage and Selection Operator (LASSO) has become increasingly popular in the analysis of high dimensional data. With LASSO, only a small number of the regression coefficients are believed to have a non-zero value, and therefore allowed to enter the model; other coefficients are while others are shrunk to zero. Aim: Determine the non-zero regression coefficients in models predicting patients’ classification (Normal, mild cognitive impairment (MCI), or Alzheimer’s) using both non-ordinal and ordinal LASSO. Methods: Pre-processed high dimensional MRI data of the Alzheimer’s Disease Neuroimaging Initiative was analyzed. Predictors of the following model were differentiated: Alzheimer’s vs. normal, Alzheimer’s vs. normal and MCI, Alzheimer’s and MCI vs. Normal. Cross-validation followed by ordinal LASSO was executed on these same sets of models. Results: Results were inconclusive. Two brain regions, frontal lobe and putamen, appeared more frequently in the models than any other region. Non-ordinal multinomial models performed better than ordinal multinomial models with higher accuracy, sensitivity, and specificity rates. It was determined that majority of the models were best suited to predict MCI status than the other two statues. Discussion: In future research, the other stages of the disease, different statistical analysis methods, such as elastic net, and larger samples sizes should be explored when using brain MRI for Alzheimer’s disease classification.

For the case where L is an ecl-premonoid, we explore various characterizations of SL-topological spaces, in particular characterization in terms of a convergence function lim: FS L(X) ! LX. We find we have to introduce a new axiom , L on the lim function in order to completely describe SL-topological spaces, which is not required in the case where L is a frame. We generalize the classical Kowalski and Fischer axioms to the lattice context and examine their relationship to the convergence axioms. We define the category of stratified L-generalized convergence spaces, as a generalization of the classical convergence spaces and investigate conditions under which it contains the category of stratified L-topological spaces as a reflective subcategory. We investigate some subcategories of the category of stratified L-generalized convergence spaces obtained by generalizing various classical convergence axioms.

Suppose q₁,q₂,…,qn are the generalised coordinates of a mechanical system moving with constraints expressed by r non-integrable equations (r〈n) (1) [equation omitted] where the dots denote differentiation with respect to the time t, and fα are nonlinear in the q’s. The equations (1) are said to represent nonlinear nonholonomic constraints and the system moving with such constraints is called nonlinear nonholonomic. From a purely analytical point of view, the author has obtained the equations of motion for a nonlinear nonholonomic mechanical system in many a different form. The importance of these forms lies in their simplicity and novelty. Some of these forms are deduced from the principle of d'Alembert-Lagrange using the definition of virtual (possible) displacements due to Četaev [ll] . The others are obtained as a result of certain transformations. Moreover, these different forms of equations of motion are written either in terms of the generalised coordinates or in terms of nonlinear nonholonomic coordinates introduced by V.S. Novoselov [23]. These forms involve the energy of acceleration of the system or the kinetic energy or some new functions depending upon the kinetic energy of the system. Two of these new functions, denoted by R (Sec. 2.3) and K (Sec. 2.4), can be identified, to a certain approximation, with the energy of acceleration of the system and the Gaussian constraint, respectively. An alternative proof (Sec.2.5) is given to the fact that, if virtual displacements are defined in the sense of N.G. Četaev [ll], the two fundamental principles of analytical dynamics - the principle of d'Alembert-Lagrange and the principle of least constraint of Gauss -are consistent. If the1 constraints are rheonomic but linear, a generalisation of the classical theorem of Poisson is obtained in terms of quasi-coordinates and the generalised Poisson's brackets introduced by V.V. Dobronravov [17]. The advantage of the various novel forms for the equations of motion is illustrated by solving a few problems. / Science, Faculty of / Mathematics, Department of / Graduate

This manuscript consists of three papers which formulate novel generalized linear model methodologies. In Chapter 1, we introduce a variant of the traditional concordance statistic that is associated with logistic regression. This adjusted c − statistic as we call it utilizes the differences in predicted probabilities as weights for each event/non- event observation pair. We highlight an extensive comparison of the adjusted and traditional c-statistics using simulations and apply these measures in a modeling application. In Chapter 2, we feature the development and investigation of three model selection criteria based on cross-validatory c-statistics: Model Misspecification Pre- diction Error, Fitting Sample Prediction Error, and Sum of Prediction Errors. We examine the properties of the corresponding selection criteria based on the cross- validatory analogues of the traditional and adjusted c-statistics via simulation and illustrate these criteria in a modeling application. In Chapter 3, we propose and investigate an alternate approach to pseudo- likelihood model selection in the generalized linear mixed model framework. After outlining the problem with the pseudo-likelihood model selection criteria found using the natural approach to generalized linear mixed modeling, we feature an alternate approach, implemented using a SAS macro, that obtains and applies the pseudo-data from the full model for fitting all candidate models. We justify the propriety of the resulting pseudo-likelihood selection criteria using simulations and implement this new method in a modeling application.

This dissertation presents results about computations of Graev metrics on free groups and characterizes isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces. In Chapter 2, computations of Graev metrics are performed on free groups. One of the related results answers an open question of Van Den Dries and Gao. In Chapter 3, isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces are characterized. The notion of generalized tree is defined and a correspondence between the isomorphism group of a generalized tree and the isometry group of a Heine-Borel Polish ultrametric space is established. The concept of a weak inverse limit is introduced to capture the characterization of isomorphism groups of generalized trees. In Chapter 4, partial results of isometry groups of uncountable compact ultrametric spaces are given. It turns out that every compact ultrametric space has a unique countable orbital decomposition. An orbital space consists of disjoint orbits. An orbit subspace of an orbital space is actually a compact homogeneous ultrametric subspace.

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Wildfires in the United States present a complexity of problems for private landowners and policy makers. This thesis takes a look at two key issues faced by private and government stakeholders; the first being a lack of knowledge regarding current prescribed fire laws and regulations. A legal review of administrative laws and regulations for prescribed burning in the Southeastern United States in the context of management-based regulation is used to address this issue. It was found that regulation for prescribed burning has shifted to a more management–based regime. The second is an empirical study of wildfire distribution in the state of Mississippi. Wildfires appear to fit a Pareto distribution throughout the state given a certain threshold. When analyzed in conjunction both studies could aid lawmakers in projecting the effects of a given policy change on actual wildfire occurrences and distribution.