  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
coeffcients as well as the construction of simultaneous confidence intervals
and, therefore, provides useful methods to perform valid post-selection
inference based on the LASSO.
