Geometric aspects of deletion diagnostics in multivariate regression

Abstract

In multivariate regression, a graphical diagnostic method of detecting observations that are influential in estimating regression coefficients is introduced. It is based on the principal components and their variances obtained from the covariance matrix of the probability distribution for the change in the estimator of the matrix of unknown regression coefficients due to a single-case deletion. As a result, each deletion statistic obtained in a form of matrix is transformed into a two-dimensional quantity. Its univariate version is also introduced in a little different way. No distributional form is assumed. For illustration, we provide a numerical example in which the graphical method introduced here is seen to be effective in getting information about influential observations.