Asymmetric Least Squares Estimation and Testing

This paper considers estimation and hypothesis tests for coefficients of linear regression models, where the coefficient estimates are based on location measures defined by an asymmetric least squares criterion function. These asymmetric least squares estimators have properties which are analogous to regression quantile estimators, but are much simpler to calculate, as are the corresponding test statistics. The coefficient estimators can be used to construct test statistics for homoskedasticity and conditional symmetry of the error distribution, and we find these tests compare quite favorably with other commonly-used tests of these null hypotheses in terms of local relative efficiency. Consequently, asymmetric least squares estimation provides a convenient and relatively efficient method of summarizing the conditional distribution of a dependent variable given the regressors, and a means of testing whether a linear model is an adequate characterization of the typical value for this conditional distribution.