Analysis of least absolute deviation

• 成果类型: Article
• 署名作者: Chen, Kani; Ying, Zhiliang; Zhang, Hong; Zhao, Lincheng
• 署名单位: Hong Kong University of Science & Technology; Columbia University; Chinese Academy of Sciences; University of Science & Technology of China, CAS
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asm082
• 发表日期: 2008
• 页码: 107122
• 关键词: resampling method; regression; models; error

摘要

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.