An MDI Model and an Algorithm for Composite Hypotheses Testing and Estimation in Marketing

Abstract

This paper indicates how an information theoretic approach via the MDI (minimum discrimination information) statistic can be used to help provide a uniform approach to both statistical testing and estimation in various kinds of marketing analyses. Extensions to constrained versions of the MDI statistic also make it possible to test the consistency of market information with management plans or policies that can be represented in “external” constraints, i.e., constraints formulated without reference to the data base, and to estimate their impact on the market. Composite hypotheses, which are difficult to deal with by the more customary methods used in market research, can be dealt with naturally and easily via these MDI approaches. Basically MDI is more efficient than classical approaches because distribution estimation and hyopthesis testing are done simultaneously and the resulting estimates obtain regardless of the conclusion of the test. Numerical illustrations are supplied and discussed. Recent developments in mathematical programming (duality) theory and methods, which are also pertinent, are briefly examined for their bearing on still further possibilities for constrained MDI modeling.