# Scalable simultaneous inference in high-dimensional linear regression models

## TL;DR

This paper introduces a computationally efficient method for simultaneous inference in high-dimensional linear regression models using the Moore-Penrose pseudoinverse, enabling scalable analysis with reliable coverage.

## Contribution

It proposes a novel, fast inference method based on the Moore-Penrose pseudoinverse that is free of tuning parameters and effective under certain symmetry assumptions.

## Key findings

- Achieves near-nominal coverage in simulations
- Computational complexity is significantly reduced
- Regularization can improve efficiency

## Abstract

The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose pseudoinverse. Under a symmetry assumption on the available regressors, the estimators are normally distributed and accompanied by a closed-form expression for the standard errors that is free of tuning parameters. We study the numerical performance in Monte Carlo experiments that mimic the size of modern applications for which existing methods are computationally infeasible. We find close to nominal coverage, even in settings where the imposed symmetry assumption does not hold. Regularization of the pseudoinverse via a ridge adjustment is shown to yield possible efficiency gains.