Iterative Reclassification Procedure for Constructing an Asymptotically Optimal Rule of Allocation in Discriminant Analysis

Abstract

Abstract The construction of a suitable rule of allocation in the two-population discrimination problem is considered in the case where there are initially available from the populations II1, II2, n 1, n 2 observations and M unclassified observations. An iterative reclassification procedure based on the n 1 + n 3 + M observations is proposed and found asymptotically optimal when M → ∞ and n 1 and n 2 are moderately large. The case of finite M is evaluated by a Monte Carlo experiment which suggests that the proposed procedure, after only one iteration, gives a rule with smaller average risk than the usual rule based on just the n 1 + n 2 classified observations.