A Necessary Condition for the Strong Oracle Property

A problem of using a non‐convex penalty for sparse regression is that there are multiple local minima of the penalized sum of squared residuals, and it is not known which one is a good estimator. The aim of this paper is to give a guide to design a non‐convex penalty that has the strong oracle property. Here, the strong oracle property means that the oracle estimator is the unique local minimum of the objective function. We summarize three definitions of the oracle property – the global, weak and strong oracle properties. Then, we give sufficient conditions for the weak oracle property, which means that the oracle estimator becomes a local minimum. We give an example of non‐convex penalties that possess the weak oracle property but not the strong oracle property. Finally, we give a necessary condition for the strong oracle property.     

A nonparametric hypothesis test for heteroscedasticity

In this paper, a hypothesis test for heteroscedasticity is proposed in a nonparametric regression model. The test statistic, which uses the residuals from a nonparametric fit of the mean function, is based on an adaptation of the well-known Levene's test. Using the recent theory for analysis of variance when the number of factor levels goes to infinity, the asymptotic distribution of the test statistic is established under the null hypothesis of homocedasticity and under local alternatives. Simulations suggest that the proposed test performs well in several situations, especially when the variance is a nonlinear function of the predictor.     

Effects of a ball-backrest chair on the muscles associated with upper crossed syndrome when working at a VDT

This study examined the effect of a ball-backrest chair on the weakness and tightness of muscles associated with upper crossed syndrome when working at a visual display terminal (VDT). The surface electromyography (EMG) was recorded from the serratus anterior, middle trapezius, and upper trapezius muscles of 20 adults as they performed VDT work, which are known as the weakened and tightened muscles of upper crossed syndrome. The recorded signals were averaged and normalized to the mean amplitude of the EMG signal obtained during submaximal reference voluntary contractions. The significance of differences between the use of a general-purpose backrest and a ball backrest was tested by paired t-test, with the significance cutoff set at alpha=0.05. The activities of the serratus anterior and middle trapezius muscles increased and that of the upper trapezius muscle decreased when sitting in a ball-backrest chair compared to when sitting in a chair with a general-purpose backrest (p<0.05). These results indicate that the use of a ball-backrest chair reduces the risk of patients with upper crossed syndrome developing muscles soreness or injury related to overuse when working at a VDT.     

Urge to Gamble in Problem Gamblers Exposed to a Casino Environment

Cue-reactivity has received increased attention in addiction research, though not for gambling in particular. We examined cue reactivity in 18 problem gamblers by accompanying them to a gaming casino and measuring their subjective urge to gamble over a 1-h period. Half of the sample was additionally exposed to a gambling-specific negative mood induction (NMI) manipulation via guided imagery. Overall, about two-thirds of the sample reported moderate to high-gambling urges during the casino exposure. Additionally, the NMI reduced cue-reactivity. Finally, gambling urges in both groups decreased over the course of the exposure sessions. These findings suggest that a majority of problem gamblers experience the urge to gamble when exposed to gambling cues and that the intensity of these urges decrease with time, especially in the presence of a gambling-relevant NMI. Cue exposure should be studied further as a potential tool in the treatment of problem gambling.     

The life-course origins of mastery among older people

In this article, we aim to identify the sources of mastery--the understanding that individuals hold about their ability to control the circumstances of their lives. The sample for our inquiry was drawn from the Medicare beneficiary files of people 65 and older living in Washington, DC, and two adjoining Maryland counties. We find that past circumstances, particularly those reflecting status attainment and early exposure to intractable hardships, converge with stressors experienced in late life to influence elders' level of mastery. The impact of past conditions, however, does not necessarily directly affect the current mastery of older people. Instead, the effect of prior experiences on current mastery is mediated by what we refer to as life-course mastery: one's belief that one has directed and managed the trajectories that connect one's past to the present. Our analyses show that life-course mastery largely serves as the mediating channel through which individuals connect their past to their present.     

Importance of interpolation when constructing double-bootstrap confidence intervals

We show that, in the context of double-bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double-bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error.     

Small‐sphere distributions for directional data with application to medical imaging

We propose novel parametric concentric multi‐unimodal small‐subsphere families of densities for p ? 1 ≥ 2‐dimensional spherical data. Their parameters describe a common axis for K small hypersubspheres, an array of K directional modes, one mode for each subsphere, and K pairs of concentrations parameters, each pair governing horizontal (within the subsphere) and vertical (orthogonal to the subsphere) concentrations. We introduce two kinds of distributions. In its one‐subsphere version, the first kind coincides with a special case of the Fisher–Bingham distribution, and the second kind is a novel adaption that models independent horizontal and vertical variations. In its multisubsphere version, the second kind allows for a correlation of horizontal variation over different subspheres. In medical imaging, the situation of p ? 1 = 2 occurs precisely in modeling the variation of a skeletally represented organ shape due to rotation, twisting, and bending. For both kinds, we provide new computationally feasible algorithms for simulation and estimation and propose several tests. To the best knowledge of the authors, our proposed models are the first to treat the variation of directional data along several concentric small hypersubspheres, concentrated near modes on each subsphere, let alone horizontal dependence. Using several simulations, we show that our methods are more powerful than a recent nonparametric method and ad hoc methods. Using data from medical imaging, we demonstrate the advantage of our method and infer on the dominating axis of rotation of the human knee joint at different walking phases.