Title: The costs and benefits of valid inference on causal parameters in the presence of high dimensional nuisance parameters
Authors: Niloofar Moosavi - Umeå university (Sweden) [presenting]
Xavier de Luna - Umea University (Sweden)
Jenny Haggstrom - Umea University (Sweden)
Abstract: The purpose is to study estimators yielding valid inference on a low dimensional causal parameter in the presence of high dimensional nuisance parameters. Naive estimation strategies based on regularisation or a preliminary model selection stage have finite sample distributions which are badly approximated by their asymptotic distributions. To solve this problem estimators which converge uniformly in distribution over a class of DGPs allowing for the number of parameters to increase with the number of observations, have recently been proposed in the literature. Uniform asymptotic results guarantee valid inference. However, this is often obtained at the cost of variance inflation, which can be severe in some settings as our simulation results show. In particular, these procedures may yield unnecessarily wide confidence intervals. We present an estimator which converges uniformly and thereby yields valid inference, but whose implied cost in terms of variability inflation is much lower than others. Approximate sparsity conditions are necessary as in the earlier literature.