MEstimation of Multivariate Regressions
针对经典多元回归模型，提出了似不相关回归（SUR）估计的稳健替代方法，即加权M估计，其渐近协方差矩阵与SUR估计类似，并以Grunfeld投资数据为例展示了平滑“l1型”M估计的应用。
Abstract Robust alternatives to the seemingly unrelated regression (SUR) estimator of Zellner (1962) are proposed for the classical multivariate regression model. These weighted M estimators achieve an asymptotic covariance matrix analogous to that of the SUR estimator. Comparisons for the l 1, least absolute deviation, case are made with the efficient estimator in the case of elliptically contoured distributions. An example reanalyzing the Grunfeld investment data using a smooth “l 1-like” M estimator is discussed in detail. In contrast to recent work of Hampel, Ronchetti, Rousseeuw, and Stahel (1986), Rousseeuw (1987), and Oja (1983), the methods studied here are not affine equivariant; some remarks on the potential significance of this failing conclude the article.