Estimating the Linear Discriminant Function from Initial Samples Containing a Small Number of Unclassified Observations

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Abstract
Estimation of the linear discriminant function L is considered in the case where there are n 1 and n 2 observations from the populations II1 and II2 and M unclassified observations. Estimates of L using all n 1 + n 2 + M observations are proposed and evaluated in terms of the expected error rate under the assumption that M is small relative to n 1 and n 2. By appropriately weighting the sample means of the unclassified observations, an estimate of L is given which dominates the usual estimate based on just the n 1 + n 2 classified observations.