Penalized likelihood models are widely used to simultaneously select variables and estimate model parameters. However, the existence of weak signals can lead to inaccurate variable selection, biased parameter estimation, and invalid inference. Thus,
identifying weak signals accurately and making valid inferences are crucial in penalized likelihood models. In this paper, we develop a unified approach to identify weak signals and make inferences in penalized likelihood models, including the special case when the responses are categorical. To identify weak signals, we utilize the estimated selection probability of each covariate as a measure of signal strength and formulate a signal identification criterion. To construct confidence intervals, we adopt a two-step inference procedure. Extensive simulation studies show that the proposed two-step inference procedure outperforms several existing methods. We illustrate the proposed method with an application to the Practice Fusion diabetes dataset.
Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifia
ble under mild conditions. In this paper, we consider estimation of the local average treatment effect under the binary instrumental variable model. We discuss the challenges for causal estimation with a binary outcome, and show that surprisingly, it can be more difficult than the case with a continuous outcome. We propose novel modeling and estimating procedures that improve upon existing proposals in terms of model congeniality, interpretability, robustness or efficiency. Our approach is illustrated via simulation studies and a real data analysis.
We congratulate Engelke and Hitz on a thought-provoking paper on graphical models for extremes. A key contribution of the paper is the introduction of a novel definition of conditional independence for a multivariate Pareto distribution. Here, we out
line a proposal for independence and conditional independence of general random variables whose support is a general set Omega in multidimensional real number space. Our proposal includes the authors definition of conditional independence, and the analogous definition of independence as special cases. By making our proposal independent of the context of extreme value theory, we highlight the importance of the authors contribution beyond this particular context.
