Due to the increasing availability of high-dimensional empirical applications in many research disciplines, valid simultaneous inference becomes more and more important. For instance, high-dimensional settings might arise in economic studies due to very rich data sets with many potential covariates or in the analysis of treatment heterogeneities. Also the evaluation of potentially more complicated (non-linear) functional forms of the regression relationship leads to many potential variables for which simultaneous inferential statements might be of interest. Here we provide a review of classical and modern methods for simultaneous inference in (high-dimensional) settings and illustrate their use by a case study using the R package hdm. The R package hdm implements valid joint powerful and eﬃcient hypothesis tests for a potentially large number of coeﬃcients as well as the construction of simultaneous conﬁdence intervals and, therefore, provides useful methods to perform valid post-selection inference based on the LASSO.
R and the package hdm are open-source software projects and can be freely downloaded from CRAN: http://cran.r-project.org.