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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.
Bayesian approaches have become increasingly popular in causal inference problems due to their conceptual simplicity, excellent performance and in-built uncertainty quantification (posterior credible sets). We investigate Bayesian inference for avera
This paper studies inference in linear models whose parameter of interest is a high-dimensional matrix. We focus on the case where the high-dimensional matrix parameter is well-approximated by a ``spiked low-rank matrix whose rank grows slowly compar
The research described herewith is to re-visit the classical doubly robust estimation of average treatment effect by conducting a systematic study on the comparisons, in the sense of asymptotic efficiency, among all possible combinations of the estim
This paper is about the ability and means to root-n consistently and efficiently estimate linear, mean square continuous functionals of a high dimensional, approximately sparse regression. Such objects include a wide variety of interesting parameters
Bayesian and frequentist criteria are fundamentally different, but often posterior and sampling distributions are asymptotically equivalent (e.g., Gaussian). For the corresponding limit experiment, we characterize the frequentist size of a certain Ba