Simple Robust Tests for Autocorrelated Errors in Time Series Design Intervention Models

A simple, robust test for the autocorrelation parameter in an intervention time-series model (AB design) is proposed. It is analogous to the traditional tests and can easily be computed by using the freeware R. In the same way as traditional tests of autocorrelation are based on least squares (LS) fits of a linear model, our robust test is based on the highly efficient Wilcoxon fit of the linear model. We present the results of a Monte Carlo study which show that our robust test inherits the good efficiency properties of this Wilcoxon fit. Its empirical power is only slightly less than the empirical power of the least squares test over situations with normally distributed errors while it exhibited much more power over situations with error distributions having tails heavier than those of a normal distribution. It also showed robustness of validity over all null situations simulated. We also present the results of the application of our test to a real data set which illustrates the robustness of our test.     

Uniform Distributions on the Integers: A connection to the Bernouilli Random Walk

Associate to each subset of the integers its almost sure limiting relative frequency under the Bernouilli random walk, if it has one. The resulting probability space is purely finitely additive, and uniform in the sense of residue classes and shift-invariance. However, it is not uniform in the sense of limiting relative frequency.     

A uniform central limit theorem for neural network-based autoregressive processes with applications to change-point analysis

We consider an autoregressive process with a nonlinear regression function that is modelled by a feedforward neural network. First, we derive a uniform central limit theorem which is useful in the context of change-point analysis. Then, we propose a test for a change in the autoregression function which – by the uniform central limit theorem – has asymptotic power one for a large class of alternatives including local alternatives not restricted to the correctly specified model.     

A restricted subset selection procedure for Weibull populations

Consider k(k ≥ 2) two-parameter Weibull populations. We want to select a subset of the populations not exceeding m in size such that the subset contains at least ? of the t best populations. We have proposed a procedure which uses either the maximum likelihood estimators or ‘simplified’ linear estimators of the parameters. The estimators are based on type II censored data. The ranking of the populations is done by comparing their reliabilities at a certain fixed time. In selected cases the constants for the procedure are tabulated using Monte Carlo methods.     

Acknowledgement

We gratefully acknowledge the partial support of the National Institute of Environmental Health Sciences through Training Grant #T32 ESO 7018 and Research Grant #ROI ESO 2286, also the partial support of Special Projects funded by COllncil for Tobacco Research - U.S.A., Inc.     

A Note on the Partial Correlation Coefficient

The question of why a geometric or coordinate-free approach to linear models has been subordinated to an algebraic approach is considered by reviewing selected papers having a geometric slant. These begin with R.A. Fisher's 1915 paper on the distribution of the correlation coefficient and continue through William Kruskal's elegant 1975 paper on the geometry of generalized inverses. The thesis is put forward that the relative unpopularity of the geometric approach is not due to an inherent inferiority but rather to a combination of inertia, poor exposition, and a resistance to abstraction.     

HEADS UP! A nested intervention with freshmen male college students and the broader campus community to promote responsible drinking

The National Institute on Alcohol Abuse and Alcoholism developed several guidelines for effective interventions in dealing with problematic college student drinking, including targeted individual interventions paired with broader campus community involvement. The project Heads UP! combines these suggestions in an effort to intervene with high-risk first-year male college students. The objective of the program is to reduce campus alcohol-related negative events and prevent these high-risk students from developing dangerous drinking patterns throughout college. The project provides an environment that supports students in actively following the goals outlined by the intervention, and it actively impacts the overall campus by helping students make responsible drinking decisions. Promising results are forthcoming, and the authors encourage other universities to design and adopt similar campus-supported programs nested within the broader campus community that target high-risk populations on campus.