Detection of influential points by convex hull volume minimization

A method of geometrical characterization of multidimensional data sets, inc luding construction of the convex hull of the data and calculation of the v olume of the convex hull, is described. This technique, together with the c oncept of minimum convex hull volume, can be used for detection of influent ial points or outliers in multiple linear regression. An approximation to t he true concept is achieved by ordering the data into a linear sequence suc h that the volume of the convex hull of the first n terms in the sequence g rows as slowly as possible with n. The performance of the method is demonst rated on four well known data sets. The average computational complexity ne eded for the ordering is estimated by O(N2+(p-1/(p+1))) for large N, where N is the number of observations and p is the data dimension, i.e. the numbe r of predictors plus 1.