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Discrimination et classement. (Discrimination and classification). (French) Zbl 0721.62061
Techniques Stochastiques. Paris etc.: Masson. viii, 174 p. FF 140.00 (1988).
There are two central concepts in the book: discrimination and classification. The first one designates the process which answers the question: how can several populations be separated and, optionally, how to find out the best way of doing this? The second concept treats the problem of assigning a new observation to one of the populations, minimizing the risk of error. The authors present an overview of the statistical methods used for these tasks.
After the first chapter, which presents the strategy the authors adopted in using the statistical techniques, follows a chapter dedicated to the recalling of some classic results in univariate analysis of variance. Chapters three and four treat the discrimination between two and between several populations. The next chapter is dedicated to the procedures for classification.
Unlike the previous chapters, the sixth one does not suppose a normal distribution of the variables that characterize the populations: the general linear model and the model of logistic discrimination are presented.
Chapter seven is dedicated to discrimination and classification based on discrete variables. The last chapter deals with distribution-free classification procedures, that is, no assumptions on the nature of the populations are made.
The book has three appendices presenting statistical distributions and specific functions, Wilk’s criterion and alternatives, and discriminant analysis software. The bibliography is not exhaustive but contains more entries than those referred to in the text; almost one third of the titles are not quoted in the text.
The presentation is very concise due to intensive use of mathematical formalism. A background in statistics and probability theory as well as a good skill in using linear algebra notations is required in order to read the book.
The work is dedicated to mathematicians in the first place, but it is useful to all those who have to carry out analysis on several populations by means of statistical methods. It may also be noted that it is addressed to all students, teachers, researchers or engineers who want to have an overview of discrimination and classification using statistical methods.
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62-02 Research exposition (monographs, survey articles) pertaining to statistics