Adaptive estimation of binomial probabilities under misclassification

If misclassification occurs the standard binomial estimator is usually seriously biased. It is known that an improvement can be achieved by using more than one observer in classifying the sample elements. Here it will be investigated which number of observers is optimal given the total number of judgements that can be made. An adaptive estimator for the probability of interest is introduced which uses an estimator of this optimal number of observers, obtained without additional cost. Some simulation results are presented which suggest that the adaptive procedure performs quite well.