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Discrimination par l’ajustement de variables indicatrices. (French) Zbl 0557.62061

Summary: Among multivariate statistical methods, discrimination is still a wide opened field. A possible way to deal with that problem consists in estimating the probability to belong to a definite population for an individual. Our purpose is to describe a method giving linear estimates of these probabilities with linear regression. This method has already been proposed and called ”Multivariate Nominal scale Analysis” (M.N.A.) but the approach presented will allow to consider each subject as a point of a (k-1)-dimensional space (for a discrimination over k groups). Furthermore this approach gives convenient rules to allocate a new individual to one of the k populations. The categories of the qualitative variables can also be graphically displayed as points in the (k-1)- dimensional space and quantitative variables can be introduced among the explanatory variables. We also study how unbalanced groups can be taken into account and, finally, an example is discussed.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
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References:

[1] F.M. Andrews et R.C. Messenger ( 1973 ). - ” Multivariate Nominal Scale Analysis : A report on a new analysis technique and a computer pro-gram ”, Survey Research Letter , Institute for Social Research, University of Michigan , Ann Arbor, Michigan .
[2] D.R. Cox ( 1970 ). - The Analysis of Binary Data , Methuen , Londres . MR 282453 | Zbl 0199.53301 · Zbl 0199.53301
[3] J.J. Daudin ( 1978 ). -” Etude de la liaison entre variables aléatoires - Régression sur variables qualitatives ”, Thèse de 3e cycle, Université Paris XI .
[4] N.E. Day et D.F. Kerridge ( 1967 ). - ” A general maximum likelihood discriminant ”, Biometrics , Vol. 23 , pp. 313 - 323 .
[5] J.M. Devaud ( 1982 ).-” Discrimination et description sur variables qualitatives - Application à des données d’accidents de travail ”, Thèse de 3e cycle, Université de Paris-Dauphine .
[6] M. Goldstein et W.R. Dillon ( 1978 ). - Discrete discriminant analysis , John Wiley and Sons , New York . MR 478475 | Zbl 0396.62042 · Zbl 0396.62042
[7] L. Lebart , A. Morineau et N. Tabard ( 1977 ). - Techniques de la description statistiaue - Méthodes et logiciels pour l’analyse des grands tableaux , Dunod , Paris .
[8] J.N. Morgan et J.A. Sonquist ( 1963 ). - ” Problems in the analysis of survey data, and a proposal ”, JASA , Vol. 58 , n^\circ 302 . Zbl 0114.10103 · Zbl 0114.10103
[9] J.P. Nakache ( 1980 ). - ” Méthodes de discrimination sur variables de nature quelconque - Théorie et pratique ”, Thèse d’Etat, Université Paris VI .
[10] C.R. Rao ( 1973 ). - Linear statistical inference and its applications , John Wiley and Sons , New York , 2nd edition. MR 346957 | Zbl 0256.62002 · Zbl 0256.62002
[11] J.M. Romeder . ( 1973 ). - Méthodes et programmes d’analyse discriminante , Dunod , Paris . Zbl 0296.62044 · Zbl 0296.62044
[12] G. Saporta ( 1977 ). - ” Une méthode et un programme d’analyse discriminante pas à pas sur variables qualitatives ”, Colloque IRIA : Analyse des données et informatique, Vol. 1 , pp. 201 - 210 .
[13] M. Tenenhaus et J.M. Bouroche ( 1970 ). - ” Quelques méthodes de segmentation ”, RIRO , Vol. 5 , n^\circ 2 , pp. 29 - 42 . Numdam | Zbl 0321.62068 · Zbl 0321.62068
[14] J. Ulmo ( 1973 ). - ” Différents aspects de l’analyse discriminante ”, Rev. Stat. Appl. , Vol. 21 , n^\circ 2 , pp. 17 - 55 . Numdam
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