DETECTION OF INFLUENTIAL OBSERVATION VECTORS FOR MULTIVARIATE LINEAR REGRESSION

Authors : B ALTUNKAYNAK, M EKNİ

Pages : 139-151

View : 19 | Download : 7

Publication Date : 2001-12-01

Article Type : Research Paper

Abstract :In this study, the influence 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 first 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 difference, 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 influential observations using the generalized Cook`s distance. The first two stages in the study facilitate the calculation of the difference between parameter estimates, while the third aids the easy determination of the observational vectors influential on the regression co- effcients. In the final section of the study, the calculations are illustrated using a numerical example.
Keywords : In°uential observation, generalized Cook`s distance, multivariate linear regression, linear restriction, projection theory