Valid simultaneous inference in high-dimensional settings (with the HDM package for R)

Abstract

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.

Using Double Machine Learning to Understand Nonresponse in the Recruitment of a Mixed-Mode Online Panel

“…Our goal is to perform valid inference on the treatment parameter α0 in a high-dimensional setting, that is, the number of variables p might be larger than the number of observations n. For ease of exposition, we consider the case of one treatment variable here, but several treatment variables can just as easily be considered and the effects estimated at the same time. If the number of variables or hypotheses to test becomes large, methods from simultaneous inference may be applied (for a survey on recent developments, we refer to Bach et al, 2018b). The unconfoundedness assumption or exogeneity assumption is given by EðεjD, XÞ ¼ 0 which denotes the identification strategy.…”