Variance estimates and hypothesis tests in least absolute value regression

Abstract

This study uses Monte Carlo simulation to examine variance estimators for the coefficient estimates in least absolute value (LAV) regression. Variance estimators examined in this article are based on a procedure suggested by McKean and Schrader [McKean, J. and Schrader, R., 1987, Least absolute errors analysis of variance In: Dodge, Y. (Ed.) Statistical Data Analysis Based on the L ₁-Norm and Related Methods, pp. 297–305.]. The variance estimates are used in significance tests for LAV regression coefficients. The resulting tests are compared on the basis of observed level of significance and power, and the test performance is used as a guide to choice of the variance estimate. Two of the factors in the Monte Carlo simulation, sample size and number of independent variables, are investigated over a wider range of values than in previous studies. The preferred variance estimator differs slightly from the one typically recommended in recent literature.

Keywords:

• Robust regression
• L ₁-Regression
• Least absolute deviations
• Monte Carlo simulation

Additional information

Notes on contributors

Terry E. Dielman

Tel.:[phone]; Email: [email protected]