A simple approximation of the sampling distribution of least absolute residuals regression estimates

Abstract

For multivariate regression with a symmetric disturbance distribution, the error in the least absolute residuals estimator is approximately multivariate normally distributed with mean zero and variance matrix λ²(X′X)⁻¹, where X is the matrix of K explanatory variables and T observations, and λ ²/T is the variance of the median of a sample of size T from the disturbance distribution. The approximate sampling theory is validated by extensive Monte Carlo studies, and some directions of possible refinement emerge.