Main Outcome Measure(s): Biomechanical variables (linear acceleration, rotational acceleration, jerk, force, impulse, and impact duration) related to head impacts were categorized by session type, player position, and helmet impact location.Results: Differences in grouping variables were found for each impact descriptor. Impacts occurred more frequently and with greater intensity during games. Linear acceleration was greatest in defensive linemen and offensive skill players and when the impact occurred at the top of the helmet. The largest rotational acceleration occurred in defensive linemen and with impacts to the front of the helmet. Impacts with the highestmagnitude jerk, force, and impulse and shortest duration occurred in the offensive skill, defensive line, offensive line, and defensive skill players, respectively. Top-of-the-helmet impacts yielded the greatest magnitude for the same variables.Conclusions: We are the first to provide a biomechanical characterization of head impacts in an interscholastic football team across a season of play. The intensity of game play manifested with more frequent and intense impacts. The highest-magnitude variables were distributed across all player groups, but impacts to the top of the helmet yielded the highest values. These high school football athletes appeared to sustain greater accelerations after impact than their older counterparts did. How this finding relates to concussion occurrence has yet to be elucidated.Key Words: concussions, mild traumatic brain injuries, Head Impact Telemetry System, acceleration Key Points N The mean linear acceleration resulting from impacts recorded during both high school games and practices exceeded that reported at the collegiate level.N Impacts to the top of the head yielded the greatest linear acceleration and impact force magnitude. Coaches must teach proper tackling techniques in order to reduce the risk of concussions and serious cervical spine injuries.

We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus making it more flexible to accommodate heterogeneity; (2) it is model-free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space. Our nonlinear independence screening procedure employs spline approximations to model the marginal effects at a quantile level of interest. Under appropriate conditions on the quantile functions without requiring the existence of any moments, the new procedure is shown to enjoy the sure screening property in ultra-high dimensions. Furthermore, the quantile-adaptive framework can naturally handle censored data arising in survival analysis. We prove that the sure screening property remains valid when the response variable is subject to random right censoring. Numerical studies confirm the fine performance of the proposed method for various semiparametric models and its effectiveness to extract quantile-specific information from heteroscedastic data.

In statistical analyses the complexity of a chosen model is often related to the size of available data. One important question is whether the asymptotic distribution of the parameter estimates normally derived by taking the sample size to infinity for a fixed number of parameters would remain valid if the number of parameters in the model actually increases with the sample size. A number of authors have addressed this question for the linear models. The component-wise asymptotic normality of the parameter estimate remains valid if the dimension of the parameter space grows more slowly than some root of the sample size. In this paper, we consider M-estimators of general parametric models. Our results apply to not only linear regression but also other estimation problems such as multivariate location and generalized linear models. Examples are given to illustrate the applications in different settings. Academic PressAMS 1991 subject classifications: primary 62F12, 62J05; secondary 60F15, 62F35.

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