Constrained General Regression in Pseudo-Sobolev Spaces with Application to Option Pricing

State price density (SPD) contains important information concerning market expectations. In existing literature, a constrained estimator of the SPD is found by nonlinear least squares in a suitable Sobolev space. We improve the behavior of this estimator by implementing a covariance structure taking into account the time of the trade and by considering simultaneously both the observed Put and Call option prices.isotonic regression, Sobolev spaces, monotonicity, multiple observations, covariance structure, option price

A comparison of HIV/AIDS-related stigma in four countries: Negative attitudes and perceived acts of discrimination towards people living with HIV/AIDS

HIV/AIDS-related stigma and discrimination have a substantial impact on people living with HIV/AIDS (PLHA). The objectives of this study were: (1) to determine the associations of two constructs of HIV/AIDS-related stigma and discrimination (negative attitudes towards PLHA and perceived acts of discrimination towards PLHA) with previous history of HIV testing, knowledge of antiretroviral therapies (ARVs) and communication regarding HIV/AIDS and (2) to compare these two constructs across the five research sites with respect to differing levels of HIV prevalence and ARV coverage, using data presented from the baseline survey of U.S. National Institute of Mental Health (NIMH) Project Accept, a four-country HIV prevention trial in Sub-Saharan Africa (Tanzania, Zimbabwe and South Africa) and northern Thailand. A household probability sample of 14,203 participants completed a survey including a scale measuring HIV/AIDS-related stigma and discrimination. Logistic regression models determined the associations between negative attitudes and perceived discrimination with individual history of HIV testing, knowledge of ARVs and communication regarding HIV/AIDS. Spearman's correlation coefficients determined the relationships between negative attitudes and perceived discrimination and HIV prevalence and ARV coverage at the site-level. Negative attitudes were related to never having tested for HIV, lacking knowledge of ARVs, and never having discussed HIV/AIDS. More negative attitudes were found in sites with the lowest HIV prevalence (i.e., Tanzania and Thailand) and more perceived discrimination against PLHA was found in sites with the lowest ARV coverage (i.e., Tanzania and Zimbabwe). Programs that promote widespread HIV testing and discussion of HIV/AIDS, as well as education regarding and universal access to ARVs, may reduce HIV/AIDS-related stigma and discrimination

Multivariate Statistics : Exercises and Solutions

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A 6-Year Follow-Up of Fracture Incidence and Volumetric Bone Mineral Density Development in Girls With Turner Syndrome

Context: Patients with Turner syndrome (TS) are at risk for osteoporotic fractures. Objective: The aims of this study were to assess the incidence of clinically important fractures in girls with TS and prospectively describe the development of volumetric bone mineral density (BMD). Design: Peripheral quantitative computerized tomography (pQCT) of the radius every other year over the 6 years of observation. Setting: Government-funded university referral center. Participants: Thirty-two girls with TS, aged 6 to 16 years, were included in the analyses. Fracture incidence was compared with the data in the general population. Bone density and strength were compared with data from 185 healthy girls. Outcomes: The main clinical outcome was the fracture occurrence. The secondary outcomes were the changes in Z-scores of the bone parameters. Results: Three girls with TS sustained four fractures during 6 years of observation. The fracture rate in TS was not substantially higher than the downward-biased fracture-rate estimate from age-matched, healthy controls (P = 0.48). Whereas the trabecular BMD Z-score decreased with age (beta estimate -0.21 +/- 0.04, P < 0.001), total bone cross-sectional area correspondingly increased (+ 0.16 +/- 0.04, P < 0.001), which led to normal bone strength. A positive history of incident fractures was not significantly associated with any of the pQCT-derived bone parameters. Conclusions: Current pediatric TS patients that are treated with growth hormone and estrogens are not at risk for osteoporotic fractures. Low BMD in TS may be counterweighted by enlarged bone radius, which leads to normal bone strength at the appendicular skeleton

Dynamic balance in children with attention-deficit hyperactivity disorder and its relationship with cognitive functions and cerebellum

Background: Attention-deficit hyperactivity disorder (ADHD) is linked to the presence of motor deficiencies, including balance deficits. The cerebellum serves as an integrative structure for balance control and is also involved in cognition, including timing and anticipatory regulation. Cerebellar development may be delayed in children and adolescents with ADHD, and inconsistent reaction time is commonly seen in ADHD. We hypothesized that dynamic balance deficits would be present in children with ADHD and they would correlate with attention and cerebellar functions. Methods: Sixty-two children with ADHD and no other neurological conditions and 62 typically developing (TD) children were examined with five trials of the Phyaction Balance Board, an electronic balancing platform. Cerebellar clinical symptoms were evaluated using an international ataxia rating scale. Conners’ Continuous Performance Test was used to evaluate patterns of reaction. Results: Children with ADHD had poorer performance on balancing tasks, compared to TD children (P<0.001). They exhibited significantly greater sway amplitudes than TD children (P<0.001) in all of the five balancing trials. The effect size of the difference between the groups increased continuously from the first to the last trial. Balance score in both groups was related to the variation in the reaction time, including reaction time standard error (r =0.25; P=0.0409, respectively, r =0.31; P=0.0131) and Variability of Standard Error (r =0.28; P=0.0252, respectively, r =0.41; P<0.001). The burden of cerebellar symptoms was strongly related to balance performance in both groups (r =0.50, P<0.001; r =0.49, P=0.001). Conclusion: This study showed that ADHD may be associated with poor dynamic balance control. Furthermore, we showed that maintaining balance correlates with neuropsychological measures of consistency of reaction time. Balance deficits and impaired cognitive functioning could reflect a common cerebellar dysfunction in ADHD children