Measures and procedures for the identification of locally influential observations in linear regression

The concept of local influence was introduced by Cook (1986) and modified by Biller & Loynes (1993). Cook's local influence was motivated by the Cook measure (1977); so they only study the local influence on the regression coefficient and they are not resistant to masking and swamping effects. In this article we extend some influence measures to locally influential measures to mitigate these difficulties. We consider, too, the problem of identifying and testing multiple locally influential observations. These measures and procedures are very general methods for assessing the influence if local departures from assumptions in likelihood-based models (not necessarily regression models).