We present a (selective) review of recent frequentist high-dimensional inference methods for constructing $p$-values and confidence intervals in linear and generalized linear models. We include a broad, comparative empirical study which complements the viewpoint from statistical methodology and theory. Furthermore, we introduce and illustrate the R-package hdi which easily allows the use of different methods and supports reproducibility.
"High-Dimensional Inference: Confidence Intervals, $p$-Values and R-Software hdi." Statist. Sci. 30 (4) 533 - 558, November 2015. https://doi.org/10.1214/15-STS527