A general framework for locating hyperplanes to fitting set of points

Abstract

This paper presents a family of new methods for locating/fitting hyperplanes with respect to a given set of points. We introduce a general framework for a family of aggregation criteria of different distance-based errors. The most popular methods found in the specialized literature can be cast within this family as particular choices of the errors and the aggregation criteria. Mathematical programming formulations for these methods are stated and some interesting cases are analyzed. It is also proposed a new goodness of fitting index which extends the classical coefficient of determination. A series of illustrative examples and extensive computational experiments implemented in R are provided to show the performances of some of the proposed methods.