The problem of estimating linear functionals based on Gaussian observations is considered. Probabilistic error is used as a measure of accuracy and attention is focused on the construction of adaptive estimators which are simultaneously near optimal under probabilistic error over a collection of...

The coherence of a random matrix, which is defined to be the largest magnitude of the Pearson correlation coefficients between the columns of the random matrix, is an important quantity for a wide range of applications including high-dimensional statistics and signal processing. Inspired by...

Abstract We address several questions relating to the use of standard regression and Structural Nested Mean Model (SNMM) approach (e. g., Ten Have et al. 2007) to analyze post-randomization effect modifiers of the intent-to-treat effect of a randomized intervention on a subsequent outcome,...

In assessing the mechanism of treatment efficacy in randomized clinical trials, investigators often perform mediation analyses by analyzing if the significant intent-to-treat treatment effect on outcome occurs through or around a third intermediate or mediating variable: indirect and direct...

Clustered treatment assignment occurs when individuals are grouped into clusters prior to treatment and whole clusters, not individuals, are assigned to treatment or control. In randomized trials, clustered assignments may be required because the treatment must be applied to all children in a...

In a case-referent study, cases of disease are compared to noncases with respect to their antecedent exposure to a treatment in an effort to determine whether exposure causes some cases of the disease. Because exposure is not randomly assigned in the population, as it would be if the population...

In an observational study of treatment effects, subjects are not randomly assigned to treatment or control, so differing outcomes in treated and control groups may reflect a bias from nonrandom assignment rather than a treatment effect. After adjusting for measured pretreatment covariates,...