Recursive Implementation of a Two-Step Nonparametric Decision Rule

The two-step approach to nonparametric discrimination is that of estimating class-conditional densities and deriving the Bayes decision rule as if the estimates were true. Direct implementation of such a decision rule ecounters two computational problems. Complexity increases with sample size, and finite precision limits the decision rule domain. Here a recursive algorithm to reduce the expected number of operations and word-length limitations below that of the direct approach is developed. A special case of the formulation reduces to the weighted k-nearest-neighbor rule.