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Analysis of least absolute deviation

Authors Chen, Kani View this author's profile
Ying, Zhiliang
Zhang, Hong
Zhao, Lincheng
Issue Date 2008
Source Biometrika , v. 95, (1), 2008, MAR, p. 107-122
Summary We develop a unified L-1-based analysis-of-variance-type method for testing linear hypotheses. Like the classical L-2-based analysis of variance, the method is coordinate-free in the sense that it is invariant under any linear transformation of the covariates or regression parameters. Moreover, it allows singular design matrices and heterogeneous error terms. A simple approximation using stochastic perturbation is proposed to obtain cut-off values for the resulting test statistics. Both test statistics and distributional approximations can be computed using standard linear programming. An asymptotic theory is derived for the method. Special cases of one-and multi-way analysis of variance and analysis of covariance models are worked out in detail. The main results of this paper can be extended to general quantile regression. Extensive simulations show that the method works well in practical settings. The method is also applied to a dataset from General Social Surveys.
ISSN 0006-3444
Language English
Format Article
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