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This paper considers estimation and testing using location measures for regression m odels that are based on an asymmetric least-squares criterion functio n. These estimators have properties that are analogous to regression quantiles, but are easier to calculate, as are the corresponding test statistics. Asymmetric least-squares tests of homoskedasticity and s ymmetry compare quite favorably with other tests of these hypotheses in terms of asymptotic relative efficiency. Consequently, asymmetric least-squares estimation provides a convenient and relatively efficie nt method of characterizing the conditional distributi on of a dependent variable given some regressors. Copyright 1987 by The Econometric Society.
Newey et al. (1987) studied this question.