Medical Diagnosis with Non-Parametric Allocation Rules

  • N. Victor
Conference paper
Part of the Lecture Notes in Medical Informatics book series (LNMED, volume 9)


In experiments with automatic diagnosis, parametric models have been employed very often even when the presuppositions were lacking and prognoses concerning the expected error rate were sometimes established on the basis of the model presuppositions. The prognoses very often proved to be false (i.e. too favourable): one reason for this optimistic bias lies in the fact that the prognoses are given mostly without verifying whether the presuppositions are fulfilled for the problem at hand. As a result of this loose management with mathematical models, the automatic diagnostic-aid has fallen into discredit. As there is usually little information concerning the distribution of the variables as regards medical problems, the non- parametric case assumes a special meaning for medical application and particularly for diagnostic problems on the basis of random vectors with unknown distribution function. The suitable mathematical model for this situation is to be sought in the class of non-parametric allocation rules.


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  1. Aitchison, J. and Aitken, C.G.G. Multivariate Binary Discrimination by the Kernel Method. Biometrika 63: 413–420, 1976.CrossRefMATHMathSciNetGoogle Scholar
  2. Breiman, L., Meisel, W., and Puree!1, E. Variable Kernel Estimates of Multivariate Densities. Technometrics 19; 135–144, 1977.CrossRefMATHGoogle Scholar
  3. Fix, E., and Hodges, J.L. Jr. Nonparametric Discrimination: Consistency Properties. U.S. Air Force School of Aviation Med., Project No. 21-49-004, Report # 4. 1951.Google Scholar
  4. Glick, N. Sample-Based Classification Procedures Derived from Density Estimators. J. Am. Statist. Assoc. 67: 116–122, 1972.CrossRefMATHGoogle Scholar
  5. Goldstein, M. Comparison of Some Density Estimate Classification Procedures. J. Aner. Statist. Assoc. 70: 666–669, 1975.CrossRefMATHGoogle Scholar
  6. Habbema, J.D.F., Hermans, J., and Van Den Broek, K. A Stepwise Discriminant Analysis Program Using Density Estimation. In Bruckmann, G. (ed.) COMPSTAT 1974. Physica-Verlag, Wien, pp. 101, 110, 1974.Google Scholar
  7. Hermans, J., and Habbema, J.D.F. Comparison of Five Methods to Estimate Posterior Probabilities. EDV in Med. u. Biol. 6: 14–19, 1975.Google Scholar
  8. Parzen, E. On Estimation of a Probability Density Function and Mode. Ann. Math. Statist. 33: 1065–1076, 1962.CrossRefMATHMathSciNetGoogle Scholar
  9. Patrick, E.A., Stelmack, F.P., and Shen, L.Y.N. Review of Pattern Recognition in Medical Diagnosis and Consulting Relative to New System Model. IEEE Trans. Systems, Man and Cyben. SMC-4: 1–16, 1974.Google Scholar
  10. Rosenblatt, M. Remarks on Some Nonparametric Estimates of a Density Function. Ann. Math. Statist. 27; 832–835, 1956.CrossRefMATHMathSciNetGoogle Scholar
  11. Victor, N. Non-parametric Allocation Rules. In: De Dombal, F.T., and Gremy, F. (eds.): Decision Making and Medical Care. North-Holland Pub!. Comp., Amsterdam, pp. 515–527, 1976.Google Scholar
  12. Victor, N. Alternativen zum klassischen Histogramm. Meth. Inform. Med. 17; 120–126, 1978.Google Scholar
  13. Wagner, T.J. Nonparametric Estimates of Probability Densities. IEEE Trans. Inform. Theory, IT-21: 438–440, 1975.Google Scholar
  14. Wertz, W. Empirische Betrachtungen und Normal approximation bei Dichteschätzungen. Operations Research-Verfahren 13: 430–433, 1972.Google Scholar

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© Online Conferences Ltd., Uxbridge, England 1981

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  • N. Victor

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