Analyzing linear regression models with hints and the dempster-shafer theory

Abstract

The aim of this work is to present an analysis of classical linear regression models based on the ideas and principles of the Dempster-Shafer theory of evidence. Assumption-based reasoning plays a central role in the analysis, and the theory of hints is used to represent the results. We start by presenting a general class of statistical models called functional models. Assumption-based reasoning is then applied to these models. A concrete example with both one and two observations illustrates the theory. Finally, generalized linear regression models are considered as instances of functional models. The comparison of the results with those obtained by least squares estimation is very interesting. © 2003 Wiley Periodicals, Inc.