Approximating the inverse of a symmetric positive definite matrix

AbstractIt is shown for an n × n symmetric positive definite matrix T = (ti, j with negative off-diagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, uniformly to order l/n2, by a matrix S = (si, j), where si,j = δi,j/ti,j + 1/t.., δi,j being the Kronecker delta function, and t.. being the sum of the elements of T. An explicit bound on the approximation error is provided

On the theory of elliptically contoured distributions

The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity. These distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg [5] on spherically symmetric distributions. It is shown that the conditional distributions of elliptically contoured distributions are elliptically contoured, and the conditional distributions are precisely identified. In addition, a number of the properties of normal distributions (which constitute a type of elliptically contoured distributions) are shown, in fact, to characterize normality

Familial and Individual Risk Markers for Physical and Psychological Dating Violence Perpetration and Victimization Among College Students

Dating violence (DV) is a prominent problem among college students that can result in harmful physical and mental health outcomes. Though much research has focused on physical DV, fewer studies have examined psychological DV. As such, the current paper compared early/familial risk markers (e.g., child physical abuse, witnessing parental violence, and maternal relationship quality) and individual risk markers (e.g., alcohol use, marijuana and prescription drug use) for physical and psychological DV among college students. Data were gathered at two large public universities using pencil and paper surveys (N = 1,482). Bivariate results revealed more risk markers for men (e.g., more child physical abuse, more frequent drinking, more close friends who drink and more marijuana and prescription drug use) compared to women. Multivariate results showed that familial risk markers were generally most important for explaining physical DV victimization and perpetration whereas individual risk markers were more salient for explaining psychological DV victimization and perpetration. Findings highlight the contribution of both early/familial and individual risk markers for understanding psychological and physical DV victimization and perpetration among college students

Lower Bounds for Average Sample Number of Sequential Multihypothesis Tests

1 online resource (PDF, 44 pages

A Class of Sequential Procedures for Choosing One of K Hypotheses Concerning the Unknown Drift Parameter of the Wiener Process

1 online resource (PDF, 20 pages

A Sequential Three Hypothesis Test for Determining the Mean of a Normal Population with Known Variance

1 online resource (PDF, 24 pages

Risk Factors for Forced, Incapacitated, and Coercive Sexual Victimization Among Sexual Minority and Heterosexual Male and Female College Students

Although college students are at high risk for sexual victimization, the majority of research has focused on heterosexual students and often does not differentiate by victimization type. Thus, little is known about prevalence rates and risk factors for sexual victimization among sexual minority college students and whether the interaction between gender and sexual orientation differs by victimization type. To address these gaps, we examine whether risk factors for three types of sexual victimization (i.e., forced, incapacitated, and coerced) differ by gender (n = 681 males; n = 732 females) and sexual orientation (n = 1,294 heterosexual; n = 119 sexual minority) and whether the intersection of gender and sexual orientation is correlated with these three types of sexual victimization among 1,413 college students. Prevalence rate results revealed significant differences between gender and sexual orientation: Sexual minority females had the highest rates of coerced sexual victimization (58%), and their mean was significantly different from the other three groups (i.e., heterosexual females, heterosexual males, and sexual minority males). For both forced and incapacitated sexual victimization, heterosexual males had significantly lower means than the other three groups. Logistic regression results revealed that child sexual abuse increased the odds of experiencing both forced and coerced sexual victimization for both heterosexual and sexual minority students, whereas increased rates of risky sexual behavior were associated with forced and incapacitated sexual victimization but only for heterosexuals. Finally, heavy drinking increased the odds of experiencing incapacitated sexual victimization for both heterosexuals and sexual minorities

Poor Parenting, Attachment Style, and Dating Violence Perpetration among College Students

Although dating violence is prevalent among college students, little is known about how both attachment style and participation in risky behaviors contribute to this pattern of violence. To address this literature gap, we examine the role of poor parenting, child abuse, attachment style, and risky sexual and drug use behaviors on dating violence perpetration among 1,432 college students (51% female). Path analysis results revealed that females were more likely to report greater attachment anxiety but lower attachment avoidance compared with males. Correlates of attachment anxiety included child physical abuse, witnessing parental violence, and poorer maternal relationship quality whereas attachment avoidant behavior was linked to more physical abuse and poorer maternal relationship quality. Females were more likely to perpetrate dating violence as were those with greater attachment anxiety and lower attachment avoidance. Other correlates of dating violence perpetration included sexual and drug risk behaviors. Finally, distal factors (i.e., more child physical abuse and poorer maternal relationship quality) also were associated with dating violence perpetration. Study implications are also discussed