DETECTION OF INFLUENTIAL OBSERVATION VECTORS FOR MULTIVARIATE LINEAR REGRESSION

In this study, the in°uence on parameter estimation of observational vec-tors in a multivariate linear regression model is investigated. A three-stage method is proposed for this investigation. The ¯rst stage involves, with the help of a linear restriction, the transformation of the multivariate lin-ear regression model into a restricted multivariate linear regression model. The second includes the calculation of the di®erence, via the projection the-ory, between parameter estimates of the multivariate linear regression model and that of the restricted multivariate linear regression model. The third contains the assessment of the in°uential observations using the generalized Cook's distance. The ¯rst two stages in the study facilitate the calculation of the di®erence between parameter estimates, while the third aids the easy determination of the observational vectors in°uential on the regression co-e±cients. In the ¯nal section of the study, the calculations are illustrated using a numerical example. Key Words: In°uential observation, generalized Cook's distance, multivariate linear regression, linear restriction, projection theory.