Online and Offline Robust Multivariate Linear Regression
arxiv(2024)
摘要
We consider the robust estimation of the parameters of multivariate Gaussian
linear regression models. To this aim we consider robust version of the usual
(Mahalanobis) least-square criterion, with or without Ridge regularization. We
introduce two methods each considered contrast: (i) online stochastic gradient
descent algorithms and their averaged versions and (ii) offline fix-point
algorithms. Under weak assumptions, we prove the asymptotic normality of the
resulting estimates. Because the variance matrix of the noise is usually
unknown, we propose to plug a robust estimate of it in the Mahalanobis-based
stochastic gradient descent algorithms. We show, on synthetic data, the
dramatic gain in terms of robustness of the proposed estimates as compared to
the classical least-square ones. Well also show the computational efficiency of
the online versions of the proposed algorithms. All the proposed algorithms are
implemented in the R package RobRegression available on CRAN.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要