Abstract
A new method for discriminating among multivariate populations, called the Hausdorff procedure, is introduced to the marketing literature. Rules for classification are defined and a limited simulation study is conducted. For the simulation, both the level of collinearity among the discriminating variables and the level of overlap among the populations are varied. The results indicate that this new procedure is particularly suitable when there is either a high degree of collinearity among the predictor variables or considerable overlap of the populations being investigated. The Hausdorff procedure is also applied to two sets of consumer data. In each instance, it is found to be superior to linear discriminant analysis with respect to the percentage of correct classifications.
Similar content being viewed by others
References
Barnsley, M. (1988).Fractals Everywhere. Boston: Academic Press.
Bernstein, I. H. (1988).Applied Multivariate Analysis. New York: Springer Verlag.
BMDP Statistical Software Manual. (1985). Berkeley: University of California Press.
Chatterjee, S., and Narayanan, A. (1992). “A New Approach to Discrimination and Classification Using a Hausdorff Type Distance,”Australian Journal of Statistics 34, 391–406.
Chatterjee, S., and Chatterjee, S. (1983). “Estimation of Misclassification Probabilities by Bootstrap Methods,”Communications in Statistics. Simulation and Computations 12, 645–656.
Cochran, W. G. (1961). “On the Performance of the Linear Discriminant Function,”Bulletin of the International Statistical Institute 39, 435–447.
Cooper, N. G. (1988).From Cardinals to Chaos. Cambridge: Cambridge University Press.
Crask, M. R., and W. D. Perrault. (1977). “Validation to Discriminant Analysis in Marketing Research,”Journal of Marketing Research 11, 60–64.
Efron, B. (1979). “Bootstrap Methods: Another Look at the Jackknife,”Annals of Statistics 7, 1–26.
Friedman, J. (1989). “Regularized Discriminant Analysis,”Journal of the American Statistical Association 84, 165–175.
IMSL Inc. (1989).STAT/LIBRARY User's Manual, Houston, Texas 1015–1016.
Lachenbruch, P. A., and M. R. Mickey. (1968). “Estimation of Error Rates in Discriminant Analysis,”Technometrics 10, 1–11.
Marco, V., D. M. Young, and D. W. Turner. (1987). “The Euclidian Distance Classifier: An Alternative to the Linear Distance Classifier,”Communications in Statistics-Simulation and Computation 16, 485–505.
McLachlan, G. J. (1987). “Error Rate Estimation in Discriminant Analysis: Recent Advances.” InAdvances in Multivariate Statistical Analysis (Ed. A. K. Gupta). Dordrecht, Holland: D. Reidel Publishing Company.
SAS Institute Inc. (1985).SAS User's Guide: Statistics, Version 5. Cary, NC: Author.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chatterjee, S., Narayanan, A. & Wiseman, F. An alternative approach to discriminating multivariate populations and its applications to marketing research. Marketing Letters 4, 349–360 (1993). https://doi.org/10.1007/BF00994353
Issue Date:
DOI: https://doi.org/10.1007/BF00994353