An influence measure known as Cook's distance has been used for judging the influence of each observation on the least squares estimate of the parameter vector. The distance does not reflect the distributional property of the change in the least squares estimator of the regression coefficients due to case deletions: the distribution has a covariance matrix of rank one and thus it has a support set determined by a line in the multidimensional Euclidean space. As a result, the use of Cook's distance may fail to correctly provide information about influential observations, and we study some reasons for the failure. Three illustrative examples will be provided, in which the use of Cook's distance fails to give the right information about influential observations or it provides the right information about the most influential observation. We will seek some reasons for the wrong or right provision of information.

No abstract

We adapt the local influence method to linear discriminant analysis for the purpose of investigating the influence of observations. A simultaneous perturbation on all observations coming from two populations is considered. We study the curvatures and the associated direction vectors of the surface formed by the perturbed maximum likelihood estimators of parameters of interest, in addition to the direction vector of the maximum slope. We show that the influence function method gives essentially the same information as the direction vector of the maximum slope. A numerical example illustrates that the local influence method gives valuable information about influential observations and outliers, even when the influence function method and the case deletion method are not adequate.

No abstract

The influence of observations on the parameter estimates for the simple structural errors-in-variables model with no equation error is investigated using the local influence method. Residuals themselves are not sufficient for detecting outliers. The likelihood displacement approach is useful for outlier detection especially when a masking phenomenon is present. An illustrative example is provided.