A New Estimator for a Population Proportion Using Group Testing

The maximum likelihood estimator is widely used in estimating the population proportion using group testing. However, it is positive biased and some alternatives have been raised in literatures. In this study, we propose a new estimator by weighted combination of order statistics. Two rules are supplied to determine the unknown weight. Using the rule of minimizing the absolute bias, our estimator is almost unbiased in most cases shown by simulations. Using the rule of minimizing the mean square error, a simple estimator with weight 1 is recommended for its good performance.