A MULTISTAGE GENERALIZATION OF THE RANK NEAREST-NEIGHBOR CLASSIFICATION RULE

We consider the problem of classifying an unknown observation from one of s (greater than or equal to 2) univariate classes (or populations) using a multi-stage left and right rank nearest neighbor (RNN) rule. We derive the asymptotic error rate (i.e., total probability of miscla ssification (TPMC)) of the m-stage univariate RNN (m-URNN) rule, and s how that as the number of stages increases, the limiting TPMC of the m -stage univariate rule decreases. Monte Carlo simulations are used to study the behavior of the m-URNN rule and compare it with the conventi onal R-NN rule. Finally, we incorporate an extension of the m-URNN rul e to multivariate observations with empirical results.