Assessment of Local Influence in Multivariate Regression with Linear Constraints

A method of detecting outliers using local influence is suggested for multivariate regression with linear constraints. It allows assessment of simultaneous perturbation affecting all the data. We consider a perturbation scheme of case-weights. This perturbation scheme simultaneously perturbs all the cases. The direction vector associated with the largest curvature of the curve at the null point provides information about outliers that cause a great change in the likelihood displacement. Observations corresponding to the component of the direction vector associated with the largest curvature that has substantially larger absolute value than the others are potential outliers. A numerical example is provided for illustration.