DETECTION OF INFLUENTIAL OBSERVATION VECTORS FOR MULTIVARIATE LINEAR REGRESSION

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.

References

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