MDI (Minimum Discrimination Information) Model and an Algorithm for Composite Hypotheses Testing and Estimation in Marketing. Revision 2.

摘要

Organizations with many different products may find it convenient to replace ad hoc statistical analyses with a uniform approach that comprehends testing and estimation. Some organizations find it imperative to move in this direction. This paper indicates how an information theoretic approach via the MDI (minimum discrimination information) statistic can be used for this purpose. 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 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 the MDI approaches. Basically MDI is more efficient than classical approaches because distribution estimation and hypothesis testing are done simultaneously. Numerical illustrations are supplied and discussed in the context of market segmentation. Developments in statistics and mathematical programming (duality) theory and methods are also briefly examined for their bearing on still further possibilities being opened for constrained MDI modeling. (Author)