We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis. Providing asymptotically valid methods for testing general linear functions of the regression parameters in high-dimensions is extremely challenging -- especially without making restrictive or unverifiable assumptions on the number of non-zero elements. We propose to test the moment conditions related to the newly designed restructured regression, where the inputs are transformed and augmented features. These new features incorporate the structure of the null hypothesis directly. The test statistics are constructed in such a way that lack of sparsity in the original model parameter does not present a problem for the theoretical justification of our procedures. We establish asymptotically exact control on Type I error without imposing any sparsity assumptions on model parameter or the vector representing the linear hypothesis. Our method is also shown to achieve certain optimality in detecting deviations from the null hypothesis. We demonstrate the favorable finite-sample performance of the proposed methods, via a number of numerical and a real data example.Comment: 42 pages, 8 figure

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We extend conformal inference to general settings that allow for time series data. Our proposal is developed as a randomization method and accounts for potential serial dependence by including block structures in the permutation scheme such that the latter forms a group. As a result, the proposed method retains the exact, model-free validity when the data are i.i.d. or more generally exchangeable, similar to usual conformal inference methods. When exchangeability fails, as is the case for common time series data, the proposed approach is approximately valid under weak assumptions on the conformity score.

We introduce new inference procedures for counterfactual and synthetic control methods for policy evaluation. Our methods work in conjunction with many different approaches for predicting counterfactual mean outcomes in the absence of a policy intervention. Examples include synthetic controls, difference-in-differences, factor and matrix completion models, and (fused) time series panel data models. The proposed procedures are valid under weak and easy-to-verify conditions and are provably robust against misspecification. Our approach demonstrates an excellent small-sample performance in simulations and is taken to a data application where we re-evaluate the consequences of decriminalizing indoor prostitution.

Many popular methods for building confidence intervals on causal effects under high-dimensional confounding require strong "ultra-sparsity" assumptions that may be difficult to validate in practice. To alleviate this difficulty, we here study a new method for average treatment effect estimation that yields asymptotically exact confidence intervals assuming that either the conditional response surface or the conditional probability of treatment allows for an ultra-sparse representation (but not necessarily both). This guarantee allows us to provide valid inference for average treatment effect in high dimensions under considerably more generality than available baselines. In addition, we showcase that our results are semi-parametrically efficient.