On Optimal Descriminants Between Two Classes of Random Variables in Terms of the Moments of Their Distributions.

摘要

For many problems of interest in statistical pattern recognition, density estimates for a random variable X of dimension d are unreliable unless the number of sample vectors is very large. Even moderately large sample sizes are often insufficient; however, lower order moments may be accurately estimated. In this paper we are concerned with the problem of optimally discriminating between two classes of random variables in terms of the available information about them of reasonable accuracy (their lower order moments). In no case do we make any assumption about the form of the probability densities of random variables X. (We do in some cases assume certain forms for the densities of functions of these random variables L(X).) (Author)