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Due to the increasing availability of high-dimensional empirical applicationsin many research disciplines, valid simultaneous inference becomes more andmore important. For instance, high-dimensional settings might arise in economicstudies due to very rich data sets with many potential covariates or in theanalysis of treatment heterogeneities. Also the evaluation of potentially morecomplicated (non-linear) functional forms of the regression relationship leadsto many potential variables for which simultaneous inferential statements mightbe of interest. Here we provide a review of classical and modern methods forsimultaneous inference in (high-dimensional) settings and illustrate their useby a case study using the R package hdm. The R package hdm implements validjoint powerful and efficient hypothesis tests for a potentially large number ofcoeffcients as well as the construction of simultaneous confidence intervalsand, therefore, provides useful methods to perform valid post-selectioninference based on the LASSO.

Valid Simultaneous Inference in High-Dimensional Settings (with the hdm package for R)