Conditional Resampling for Misclassified Multinomial Data With Applications to Sampling inspection

Abstract

A conditional resampling methodology is proposed for improving the estimators of multinomial classification probabilities in the presence of a fallible classifier. The (unbiased) estimator requires knowledge of the misclassification error rates, which are obtained by resampling from the initial sample and applying an infallible classifier. Tenenbein's “double sampling” methodology resamples randomly from the initial sample. We show that substantial gains in efficiency are obtainable if, instead of simple random resampling, different resampling rates are allowed for the fallibly determined classes in the initial sample. In most situations, this resampling methodology is neither more difficult nor more expensive than the double sampling methodology. A very promising area of application of the proposed methodology is sampling inspection in quality control, where products can either be classified quickly by inspectors or by a more thorough, perhaps destructive, inspection.

KEY WORDS:

• Classification
• Doubling sampling
• Maximum likelihood estimator
• Minimize cost; Minimum variance
• Quality control