A frequently encountered challenge in high-dimensional regression is the detection of relevant variables. Variable selection suffers from instability and the power to detect relevant variables is typically low if predictor variables are highly correlated. When taking the multiplicity of the...

We propose probabilistic lower bounds for the number of false null hypotheses when testing multiple hypotheses of association simultaneously. The bounds are valid under general and unknown dependence structures between the test statistics. The power of the proposed estimator to detect the full...