Asymptotically Optimal Approximation of Multidimensional pdf´s by Lower Dimensional pdf´s

Probability density functions (pdf´s) of high dimensionality are impractical to estimate from real data. For accurate estimation, the dimensionality of the pdf can be at most 5-10. In order to reduce the dimensionality a sufficient statistic is usually employed. When none is available, there is no universal agreement on how to proceed. We show how to construct a high-dimension pdf based on the pdf of a low-dimensional statistic that is closest to the true one in the sense of divergence. The latter criterion asymptotically minimizes the probability of error in a decision rule. An application to feature selection for classification is described