Detection of Outliers in Multivariate Regression Using Plug-in Method

Outlier detection in multivariate regression with random regressors is considered using plug-in method. We derive alternative univariate regression models under the normality assumption to which the usual robust estimation methods developed in the univariate regression can be applied. The alternative univariate regression model allows us to incorporate covariance relations among the response variables in robust estimation of the associated parameters. We then derive an identity relating parameters for the alternative univariate regression models to those for the original multivariate regression models. Robust estimators of the original multivariate regression parameters are found by plugging robust estimators of the alternative univariate regression parameters into the identity derived. The resulting robust estimators are used for outlier detection. An example is given for illustration.