Cook’s Distance

Introduction

Prior to 1975 there was little awareness within statistics or the applied sciences generally that a single observation can influence a statistical analysis to a point where inferences drawn with the observation included can be diametrically opposed to those drawn without the observation. The recognition that such influential observations do occur with notable frequency began with the 1977 publication of Cook’s Distance, which is a means to assess the influence of individual observations on the estimated coefficients in a linear regression analysis (Cook 1977). Today the detection of influential observations is widely acknowledged as an important part of any statistical analysis and Cook’s distance is a mainstay in linear regression analysis. Generalizations of Cook’s distance and of the underlying ideas have been developed for application in diverse statistical contexts. Extensions of Cook’s distance for linear regression along with a discussion of surrounding methodology...