Accession Number : AD0684495

Title :   CHEBYSHEV BOUNDS FOR RISKS AND ERROR PROBABILITIES IN SOME CLASSIFICATION PROBLEMS,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Marshall,Albert W. ; Olkin,Ingram

Report Date : JAN 1969

Pagination or Media Count : 21

Abstract : It is often the case that a random variable Y characterizes an item which is to be classified as belonging to one of several classes. When Y is expensive or impossible to observe, difficulties of classification arise and it may be desirable or necessary to classify the item on the basis of an auxiliary random variable X which is correlated with Y and may be regarded as a measure of Y. Of course, misclassification is a possibility. We assume that the loss suffered in such an event is determined by X and Y. When the joint distribution of X and Y is unknown, but only means, variances and covariance are known, the expected loss (risk) cannot be precisely computed. However, Chebyshev-type bounds for the risk can often be obtained for a given loss function. In this paper, several examples are presented which not only serve as illustrations, but which also are important in their own right. For certain kinds of classification procedures, bounds are also obtained for probabilities of misclassification. (Author)

Descriptors :   (*SEARCH THEORY, CLASSIFICATION), (*CLASSIFICATION, ERRORS), PROBABILITY, INEQUALITIES

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE