Before revision:  The proposed estimators do not require oracle property for valid inference . We propose easy-to-implement algorithms for  high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection using a new multiplier cluster bootstrap.
After revision:  The proposed estimators do not require oracle property for valid inference without requiring oracle property. We provide easy-to-implement algorithms for high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection using a new multiplier cluster bootstrap.