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Distribution-free partial discrimination procedures. (English) Zbl 0658.62072
This paper reviews discrimination procedures which provide distribution- free control over the individual misclassification probabilities. Particular emphasis is placed on the two-population rank method developed by J. D. Broffitt, R. H. Randles and R. V. Hogg [J. Am. Stat. Assoc. 71, 934-939 (1976; Zbl 0336.62047)] which utilizes the general formulation of C. P. Quesenberry and M. P. Gessaman [Ann. Math. Stat. 39, 664-673 (1968; Zbl 0162.220)]. It is shown that the rank method extends from two to three or more populations in a natural and flexible fashion. A Monte Carlo study compares two suggested extensions with others proposed by Broffitt.
MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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[1] Ambrosi, K., A distribution-free method of discriminant analysis for variables of any structure, Oper. res. verf., 35, 1-15, (1979)
[2] Beckman, R.J.; Johnson, M.E., A ranking procedure for partial discriminant analysis, J. am. stat. assoc., 76, 671-675, (1981)
[3] Broffitt, J.D.; Randles, R.H.; Hogg, R.V., Distribution-free partial discriminant analysis, J. am. stat. assoc., 71, 934-939, (1976) · Zbl 0336.62047
[4] Broffitt, J.D., Nonparametric classification, () · Zbl 0504.62049
[5] Devijver, P.A., New error bounds with the nearest neighbour rule, IEEE trans. inf. theory, IT-25, 749-753, (1979) · Zbl 0422.68043
[6] Hand, D.J., Discrimination and classification, (1981), Wiley New York · Zbl 0587.62119
[7] Hellman, M.E., The nearest neighbor classification rule with a reject option, IEEE trans. syst. sci. cybern., SSC-6, 179-185, (1970) · Zbl 0204.52201
[8] Ng, T.H., Rank procedures in discriminant analysis for two or more populations, ()
[9] Ng, T.H.; Randles, R.H., Rank procedures in many population forced discrimination problems, Comm. stat., 12, 1943-1960, (1983) · Zbl 0564.62049
[10] Quensenberry, C.P.; Gessaman, M.P., Nonparametric discrimination using tolerance regions, Ann. math. stat., 39, 664-673, (1968) · Zbl 0162.22001
[11] Randles, R.H.; Wolfe, D.A., Introduction to the theory of nonparametric statistics, (1979), Wiley New York · Zbl 0529.62035
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