Online and Offline Robust Multivariate Linear Regression

arXiv:2404.19496v1 Announce Type: cross
Abstract: 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 …

abstract aim algorithms arxiv contrast criterion gradient least linear linear regression math.st multivariate offline parameters regression regularization ridge robust square stat.ml stat.th stochastic type