Simulation-based consistent inference for biased working model of non-sparse high-dimensional linear regression

► We introduce a simulation-based procedure to reduce the bias of working model that is selected from high-dimensional model. ► The resulting estimators of the parameters in the working model are asymptotic normally distributed. ► We build simulation-based confidence regions for the parameters in the working model. ► The newly proposed estimators and confidence regions outperform existing ones in the sense of consistency.