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Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be ill-posed. The general method proceeds in a fully data-driven and adaptive way from large to small groups or singletons of covariates, depending on the signal strength and the correlation structure of the design matrix. We propose a novel hierarchical multiple testing adjustment that can be used in combination with any significance test for a group of covariates to perform hierarchical inference. Our adjustment passes on the significance level of certain hypotheses that could not be rejected and is shown to guarantee strong control of the familywise error rate. Our method is at least as powerful as a so-called depth-wise hierarchical Bonferroni adjustment. It provides a substantial gain in power over other previously proposed inheritance hierarchical procedures if the underlying alternative hypotheses occur sparsely along a few branches in the tree-structured hierarchy.
The Consent-to-Contact (C2C) registry at the University of California, Irvine collects data from community participants to aid in the recruitment to clinical research studies. Self-selection into the C2C likely leads to bias due in part to enrollees
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local heritability. Gro
Analyses of environmental phenomena often are concerned with understanding unlikely events such as floods, heatwaves, droughts or high concentrations of pollutants. Yet the majority of the causal inference literature has focused on modelling means, r
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to mode
We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur as a functi