High-Dimensional Inference: Confidence Intervals, $p$-Values and R-Software hdi

Abstract

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.Comment: Published at http://dx.doi.org/10.1214/15-STS527 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org