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

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.