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The computational complexity of simultaneous inference methods inhigh-dimensional linear regression models quickly increases with the numbervariables. This paper proposes a computationally efficient method based on theMoore-Penrose pseudoinverse. Under a symmetry assumption on the availableregressors, the estimators are normally distributed and accompanied by aclosed-form expression for the standard errors that is free of tuningparameters. We study the numerical performance in Monte Carlo experiments thatmimic the size of modern applications for which existing methods arecomputationally infeasible. We find close to nominal coverage, even in settingswhere the imposed symmetry assumption does not hold. Regularization of thepseudoinverse via a ridge adjustment is shown to yield possible efficiencygains.

Scalable simultaneous inference in high-dimensional linear regression models