Anderson's classification statistic based on a post-stratified training sample

Abstract

The performance of Anderson's classification statistic based on a post-stratified random sample is examined. It is assumed that the training sample is a random sample from a stratified population consisting of two strata with unknown stratum weights. The sample is first segregated into the two strata by post-stratification. The unknown parameters for each of the two populations are then estimated and used in the construction of the plug-in discriminant. Under this procedure, it is shown that additional estimation of the stratum weight will not seriously affect the performance of Anderson's classification statistic. Furthermore, our discriminant enjoys a much higher efficiency than the procedure based on an unclassified sample from a mixture of normals investigated by Ganesalingam and McLachlan (1978).

Keywords:

• Anderson's classification statistic
• post-stratified training sample
• mixture of normal populations
• stratum weight
• probabilities of misclassification
• overall error of joisclassification
• asymptotic efficiency