A multistage generalization of the rank nearest neighbor classification rule

Abstract We consider the problem of classifying an unknown observation from one of s (⩾ 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 misclassification (TPMC)) of the m -stage univariate RNN ( m -URNN) rule, and show that as the number of stages increases, the limiting TPMC of the m -stage univariate role decreases. Monte Carlo simulations are used to study the behavior of the m -URNN rule and compare it with the conventional k -NN rule. Finally, we incorporate an extension of the m -URNN role to multivariate observations with empirical results.