Influence Diagnostics in Modified Liu-type Estimator

Abstract

In regression, it is of interest to detect anomalous observations that exert an unduly large influence on the least squares (LS) analysis. Frequently, the existence of influential data is complicated by the presence of collinearity (see, e.g., Walker and Birch [1] ). Very little work has been done, however, on the possible effects that collinearity can have on the influence of an observation. While dealing with multicollinearity some new type of Liu estimator is proposed. When modified Liu-type estimator (MLE) is used to mitigate the effects of multicollinearity, the influence of observations can be drastically modified. In this article, we propose approximate case deletion formula to detect influential points in MLE. As an illustrative example, a real dataset is analyzed.