Thesis (Ph. D.)--University of Chicago, Dept. of Economics, June 1999. / Includes bibliographical references. Also available on the Internet.

Data regarding the severity of premenstrual symptoms were collected from three groups of women: women over age 24 years seeking care from a gynecological practitioner, undergraduates at OSU living in student dormitories, and graduate students enrolled at OSU. The symptoms evaluated were depression, tiredness, irritability, anxiety, headache, breast swelling and tenderness, craving for sweets, craving for salty foods, binge eating, and acne. Symptoms were rated on a scale of zero (not present) to three (severe). Multivariate profile analysis was used to evaluate the hypothesis that the profiles formed by the mean vectors of these premenstrual symptoms were parallel with regard to symptom severity, age, consumption of caffeinated beverages and refined sugar, maternal history of premenstrual syndrome (PMS) and recent use of oral contraceptives. Parallel profiles were further evaluated for coincidence. Results of the analysis indicated that in each of the three samples of women studied, the presence of premenstrual symptomatology was indicated by one pattern of symptom severity, and that this pattern remained constant as symptoms became more severe. The variability in the premenstrual symptoms could be explained by the inherent variability of the women studied, a finding which does not support the existence of multiple subtypes of PMS. Evidence of a positive association between age and increasing symptom severity was found only in the graduate student group. High levels of consumption of caffeine were shown to exacerbate premenstrual symptoms among the graduate students, and frequent consumption of refined sugar and "junk food" were shown to exacerbate symptoms among older women. Increased symptom severity of premenstrual symptoms in women whose mothers suffered from PMS was noted only among undergraduate students. No evidence was found to implicate oral contraceptive use in the exacerbation or amelioration of premenstrual symptoms. / Graduation date: 1992

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: cutaneous mechanoreceptors, logistical regression. Includes bibliographical references (p. 156-159).

Includes bibliographical references (p. 112-117).

The present investigation was a Monte Carlo experiment designed to evaluate the performance of several metrics in spotting correlational outliers. Specifically, the metrics that were compared were the Mahalanobis D², Bacon MLD, Carrig D, MCD, Robust PCLOW and Robust PCHIGH. This was the first comparative simulation study to include robust PCLOW and robust PCHIGH. The Mahalanobis D², MCD, Robust PCLOW and Robust PCHIGH were each applied using an approximate statistical criterion. The Carrig D and Bacon MLD were applied using a "natural drop" approach that separated scores on the metric into two groups: outlying and non-outlying. The "natural drop" utilizes a k-means algorithm from cluster analysis to separate the scores into the two groups. Both majority and contaminant observations were generated from multivariate normal distributions based on factor-analytic models. Experimental factors included majority versus contaminant communality level, majority-contaminant factor models scenario, number of variables, sample size and fraction of outliers. Results indicated that the "natural drop" method of application for the Carrig D and Bacon MLD leads to intolerably high false-alarm rates. Overall, PCLOW clearly outperformed PCHIGH. Suprisingly, PCLOW did not distinguish itself from MCD in terms of performance as expected in certain experimental conditions. The conditions in this study were limited. Future comparative studies of the metrics could include conditions of non-normality and hybrid types of outliers (i.e. outliers that are both mean shift and correlational). Despite its poor performance in this study, I theorize that robust PCHIGH could have an advantage over MCD in spotting certain kinds of mean-shift outliers. Also, research into the distributional properties of the Carrig D is warranted. / text

Recently, the study of negative dependence structures has aroused considerable interest amongst researchers in actuarial science and quantitative risk management. This thesis centres on two extreme negative dependence structures in different dimensions - counter-monotonicity and mutual exclusivity, and develops their novel characterizations and applications to risk management. Bivariate random vectors are treated in the first part of the thesis, where the characterization of comonotonicity by the optimality of aggregate sums in convex order is extended to its bivariate antithesis, namely, counter-monotonicity. It is shown that two random variables are counter-monotonic if and only if their aggregate sum is minimal with respect to convex order. This defining property of counter-monotonicity is then exploited to identify a necessary and sufficient condition for merging counter-monotonic positions to be risk-reducing. In the second part, the notion of mutual exclusivity is introduced as a multi-dimensional generalization of counter-monotonicity. Various characterizations of mutually exclusive random vectors are presented, including their pairwise counter-monotonic behaviour, minimal convex sum property, and the characteristic function of their aggregate sums. These properties highlight the role of mutual exclusivity as the strongest negative dependence structure in a multi-dimensional setting. As an application, the practical problem of deriving general lower bounds on three common convex functionals of aggregate sums with arbitrary marginal distributions is considered. The sharpness of these lower bounds is characterized via the mutual exclusivity of the underlying random variables. Compared to existing bounds in the literature, the new lower bounds proposed enjoy the advantages of generality and simplicity. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy

No description available.

No description available.

A wide array of procedures have been proposed for testing correlation pattern. Many, but not all, of the statistical techniques available for testing correlation pattern are derived under the distributional condition of multivariate normality which does not always hold in the behavioral, educational and social sciences. Though a number of studies have explored the performance of structure analysis techniques under conditions of multivariate nonnormality, very little is known about the actual performance of many correlation structure analysis techniques under conditions of multivariate nonnormality. In addition, very little is known about the actual concurrent performance of tests of multivariate normality. The present investigation ascertains how tests of correlation pattern hypotheses and indicators of multivariate normality perform when data are from multivariate normal or nonnormal parent populations. This paper reviews and examines, using a Monte Carlo simulation study, the concurrent performance of different approaches to testing (1) correlation pattern hypotheses, including, (i) normal theory (NT) and asymptotically distribution free (ADF) covariance structure analysis techniques, (ii) NT and ADF correlation structure analysis techniques, (iii) correlation pattern specific techniques; (2) the distributional assumption of multivariate normality using statistics based on Mardia's measures of multivariate skewness and kurtosis. This paper also examines the performance characteristics of test procedures based on joint consideration of tests of multivariate normality and structure analysis techniques. Performance of the covariance and correlation structure analysis techniques, tests of multivariate normality, and joint test procedures was assessed across different types of correlation pattern models, numbers of variables, levels of skew and kurtosis, sample sizes, and nominal alpha levels, on the primary Neyman-Pearson criterion for an optimal test, according to which an optimal procedure (1) controls experimentwise Type I error rate at or below the nominal level, (2) maximizes power.