Before revision:  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 and asymptotically non-conservative using a new multiplier cluster bootstrap  .
After revision:  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 and asymptotically non-conservative using a new multiplier cluster bootstrap . We then apply algorithms to study multiple-testing problem of gendered language on the internet .